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HP Calculator 10BII User's Manual

1. PMT 1 041 40 FV 10 000 00 One of the values for PV PMT FV can be zero For example following is a cash flow diagram from the saver s perspective for a savings account with a single deposit and a single withdrawal five years later Interest compounds monthly In this example PMT is zero VYR 8 00 PMT 0 00 PV 17 000 00 Time value of money calculations are described in the next chapter 50 4 Picturing Financial Problems Recognizing a Cash Flow Problem A financial problem that does not have regular uniform payments sometimes called uneven cash flows is a cash flow problem rather than a TVM problem A cash flow diagram for an investment in a mutual fund follows This is an example of a problem that is solved using either CORP Net Present Value or QE Internal Rate of Return per Year 16 567 20 5 000 00 9 10 1 5 000 00 6 000 00 7 000 00 Cash flow problems are described in chapter 6 4 Picturing Financial Problems 51 Page 52 is blank 5 Time Value of Money Calculations Using the TVM Application The time value of money TVM application is used for compound interest calculations that involve regular uniform cash flows called payments Once the values are entered you can vary one value at a time without entering all the values again To use TVM several prerequisites must be met The amount of each payment must be the same If the paym
2. Find the margin if cost is 15 00 and selling price is 22 00 OO 15 00 Enters cost AAE 22 00 Enters price 31 82 Calculates margin 1f the cost is 20 00 and the markup is 33 what is the selling price BOE 20 00 Enters cost ocw 33 00 Enters markup 26 60 Calculates price If you borrow 14 000 PV for 360 months N at 10 interest I YR what is the monthly repayment Set to End mode Press if BEGIN annunciator is displayed Keys Display Description DDAL 12 00 Sets payments per year GOON 360 00 Enters payments DTA 10 00 Enters interest per year GOO 14 000 00 Enters present value CH 0 00 Enters future value 122 86 Calculates payment if paid at end of period Wat als TVM berekeningen Het is niet nodig dat voor ieder voorbeeld de TVM waarden opnieuw worden ingevoerd Hoeveel kunt u lenen met de waarden die u zojuist hebt ingevoerd pagina 6 als u betalingen van 100 00 wilt doen Toetsen Display Beschrijving COGO 6D Eun 100 00 Voert het nieuwe bedrag van de betaling in Betaalde bedragen zijn negatief 11 395 08 Berekent het bedrag dat u kunt tenen Hoeveel kunt u lenen tegen een rente van 9 5 XCGY8 9 50 Voert de nieuwe rentevoet in 11 892 67 Berekent de nieuwe huidige waarde voor een betaling van 100 00 bij een rente van 9 596 CC GS 10 00 Voert de oorspronkelijke rente opnieuw in OOOOOR 14 000 00 Voert de oorspronkelijke hui dige waarde opnieuw in exp
3. Finding the lease payment necessary to achieve a specified yield Finding the present value capitalized value of a lease The first payment on a lease usually occurs at the beginning of the first period Thus most lease calculations use Begin mode Example Calculating a Lease Payment A customer wishes to lease a 13 500 car for three years The lease includes an option to buy the car for 7 500 at the end of the lease The first monthly payment is due the day the customer drives the car off the lot If you want to yield 10 annually compounded monthly what will the payments be Calculate the payments from your the dealer s point of view 5 Time Value of Money Calculations 63 FV 7500 00 PMT Money received by lessor is positive 1 2 35 36 VYR 1096 N 36 Money paid out PAYR 12 by lessor is negative PV 13 500 00 Begin Mode Set to Begin mode Press QED if annunciator is not displayed Keys Display Description OOOH 12 00 Sets payments per year DON 10 00 Stores desired annual yield DCMA 13 500 00 Stores lease price O00mM 7 500 00 Stores residual buy out value EO 36 00 Stores length of lease in months ED 253 99 Calculates monthly lease payment Notice that even if the customer chooses not to buy the car the lessor still includes a cash flow coming in at the end of the lease equal to the residual value of the car Whether the customer buys the car or it is sold on the open mar
4. Set to End mode Press QE if BEGIN annunciator is displayed what is the monthly repayment Keys Display ogo 12 00 GXeo 360 00 Oas 10 00 OQ OO00M 14 000 00 OM 0 00 END 122 86 14 Ata Glance Description Sets payments per year Enters number of payments Enters interest per year Enters present value Enters future value Calculates payment if paid at end of period TVM What At a Glance Display 100 00 11 395 08 It is not necessary to reenter TVM values for each example Using the values you just entered page 14 how much can you borrow if you want a payment of 100 00 Description Enters new payment amount Money paid out is negative Calculates amount you can borrow How much can you borrow at a 9 5 interest rate 0Oaa 37 COGO Gv O00m 9 50 11 892 67 10 00 14 000 00 122 86 Enters new interest rate Calculates new present value for 100 00 payment and 9 5 interest Reenters original interest rate Reenters original present valuc Calculates original payment AtaGlance 15 Amortization At a Glance LI After calculating a payment using Time Value of Money aoco TVM enter the periods to amortize and press QE SBEGEG Then press Sto continually cycle through the principal OOCCOO interest and balance values indicated by the PRIN INT Segeo and BAL annunciators respectively cose Using the previo
5. 1 Use and to enter x y pairs The j valucs are the weights of the x values 2 Press CQ Example A survey of 266 one bedroom rental apartments reveals that 54 of them rent for 500 per month 32 for 505 88 for 510 and 92 for 516 What is the average monthly rent Keys Display Description 0 00 Clears statistics memory OOOMOOH 1 00 Enters first rent and its weight GX9XS9 e G2G9 200 Enters second rent and its weight OQOOMOOH 3 00 Enters third rent and its weight GXQXG 9G9 4 00 Eaters fourth rent and its weight CH 509 44 Calculates weighted mean 7 Statistical Calculations 93 Page 94 is blank Additional Examples Business Applications Setting a Sales Price One method for setting the per unit sales pricc is to determine the cost of production per unit and then multiply by the desired rate of return For this method to be accurate you must identify all costs associated with the product The following equation calculates unit price based on total cost and rate of return PRICE TOTAL COST NUMBER OF UNITS x 1 RTN 100 Example To produce 2 000 units your cost is 40 000 You want a 20 rate of return What price should you charge per unit Keys Display Description OaS 40 000 00 Enters cost DTTA 20 00 Calculates unit cost CXOCDGCXOQX9G 24 00 Calculates unit sale COCXO price 8 Additional Examples 95 Forecasting Based on History One method of forecasti
6. End Mode Set to End mode Press Q 9 if BEGIN annunciator is displayed 5 Time Value of Money Calculations 55 Keys Display COO es 12 00 GX COGN 36 00 CX9OGUS 10 50 COGXXXO 13 000 00 TEOT om 0 00 422 58 Description Sets periods per year Stores number of periods in loan Stores annual nominal interest rate Stores amount borrowed Stores the amount left to pay after 3 years Calculates the monthly payment The negative sign indicates moncy paid out Part 2 Ata price of 14 500 what interest rate is necessary to lower your payment by 50 00 to 372 53 CX COEwD 372 53 Ge 2 03 Decreases payment from 422 53 Calculates annual interest rate for the reduced payment Part 3 If interest is 10 5 what is the maximum you can spend on the car to lower your car payment to 375 00 CXOX GS 10 50 Coocan 375 00 11 537 59 OOOGO 13 037 59 56 5 Time Value of Money Calculations Stores original interest rate Stores desired payment Calculates amount of money to finance Adds the down pay ment to the amount financed for total price of the car Example A Home Mortgage You decide that the maximum monthly mortgage payment you can afford is 930 00 You can make a 12 000 down payment and annual interest rates are currently 7 5 If you obtain a 30 year mortgage what is the maximum purchase price you can afford VYR 7 596 N 30x12 P YR 12 TOMUS 356 357 358 mm
7. money received is positive 8 Additional Examples 99 Example An investor wishes to purchase a 100 000 mortgage taken out at 9 for 20 years Since the mortgage was issued 42 monthly payments have been made The loan is to be paid in full a balloon payment at the end of its fifth year What is the yield to the purchaser if the price of the mortgage is 79 000 Step 1 Calculate PMT Make sure FV 0 Set to End Mode Press QE if BEGIN annunciator is displayed Keys Display CODD 12 00 9 00 Xo De 240 00 DOTTOR 100 000 00 om 0 00 aD 899 73 Description Sets payments per year Stores interest rate Stores number of months Stores original amount of mortgage Enters amount left to pay after 20 years Calculates regular payment Step 2 Enter the new value for N indicating when the balloon occurs then find FV the amount of the balloon Keys Display Caen 899 73 Ge 60 00 w 88 706 74 100 8 Additional Examples Description Rounds payment to two decimal places for accuracy Stores number of payments until balloon Calculates balloon payment add to final payment Step 3 Enter actual current values for N and PV then find the new I YR for the discounted mortgage with balloon Keys Display Description OOOOH 18 00 Stores remaining number of payments DOTTO 79 000 00 Stores price of mortgage v8 20 72 Calculates the return on this discounted mortgage Annual Percent
8. repeatedly to view the cash flows and number of times each occurs Now that you have entered the cash flows store the interest rate and calculate the net present value Keys Display Description Oaa 15 00 Stores annual interest rate CORP 27 199 92 Calculates net present value of stored cash flows Sec rounding example on page 59 This result shows that if you want a yield of 15 per year you should pay 27 199 92 for the contract Notice that this amount is positive The net present value is simply the summed or netted value of a series of cash flows when they are discounted to the front of the time line NPV 27 199 92 saa 1 15 per year 4 415 91 ane 7 500 00 13 579 UBS V 9 21 23 25 82 6 Cash Flow Calculations Calculating Internal Rate of Return 1 Press QED store number of periods per year in P YR 2 Enter the cash flows using and V 3 Press QED When you calculate IRR YR you get the annual nominal rate that gives an NPV of zero The following example uses the cash flows that were entered in the previous example More than one IRR YR can exist If you get the No Solution message see Appendix B page 129 Example If the seller of the contract in the previous example wants 28 000 and you accept that price what is your yicld This is an IRR YR calculation that requires a slight modification to the currently stored cash flows 10 000 l3 1 17 19 2 23 25 IRR YR
9. 0 00 Clears statistical registers 00 1 00 Enters first time Ow 2 00 Enters second time Go 3 00 Enters third time GXOXG9 4 00 Enters fourth time 0e 5 00 Enters fifth time 00Oe 6 00 Enters sixth time 3 50 Calculates the mean SED 0 85 Calculates the sample standard deviation ees 7748 Displays Zx Gom 6 00 Displays v GC 3 59 Calculates the root mean square The standard deviations calculated by QE an OE are the sample standard deviations ink assume that the data is a sampling of a larger complete set of data If the data constitutes the entire population the true population standard deviations can be calculated by pressing and EDO Example 2 The coach has four new players on the team with heights of 193 182 177 and 185 centimeters and weights of 90 81 83 and 77 kilograms Find the mean and population standard deviation of both their heights and weights then sum the y data 7 Statistical Calculations 89 Keys Display Qa 0 00 QMOOMOOH 100 CO BXZe 8900G9 2 00 COCOCDee G9 3 00 COGXSe GO 4 00 m6 184 25 im 82 75 mcm 5 80 Om 47 eu 331 00 Description Clears statistical registers Enters height and weight of player 1 Enters height and weight of player 2 Enters height and weight of player 3 Enters height and weight of player 4 Calculates mean of heights x Displays mean of weights Calculates population standard deviation for heights x Dis
10. 1 061 68 which means the annual effective interest rate is 6 168 Examples of converting between nominal and annual effective rates are on pages 72 through 73 Two Types of Financial Problems The financial problems in this manual use compound interest unless specifically stated as simple interest calculations Financial problems are divided into two groups TVM problems and cash flow problems Recognizing a TVM Problem If uniform cash flows occur between the first and last periods on the cash flow diagram the financial problem is a TVM time value of money problem There are five main keys used to solve a TVM problem Number of periods or payments Annual percentage interest rate usually the annual nominal rate Present value the cash flow at the beginning of the time line Periodic payment Future value the cash flow at the end of the cash flow diagram in addition to any regular periodic payment 8898ge 4 Picturing Financial Problems 49 You can calculate any value after entering the other four Cash flow diagrams for loans mortgages leases savings accounts or any contract with regular cash flows of the same amount are normally treated as TVM problems For example following is a cash flow diagram from the borrower s perspective for a 30 year 150 000 00 mortgage with a payment of 1 041 40 at 7 5 annual interest with a 10 000 balloon payment PV 150 000 00 N 360 GO x 12 357 358 359 360
11. COCOS 17 50 Enters number CX 20 13 Adds 15 Find the margin if the cost is 15 00 and selling price is 22 00 COGO GSP 15 00 Enters cost PAm 22 00 Enters price 31 82 Calculates margin Tf the cost is 20 00 and the markup is 33 what is the selling price oew 20 00 Enters cost aow 33 00 Enters markup RO 26 60 Calculates price 12 AtaGlance Memory Keys At a Glance Stores a constant operation Stores a value in the M register memory location Recalls a value from the M register Adds a value to the number stored in the M register Stores a value in a numbered register Recalls a value from a numbered register Multiply 17 22 and 25 by 7 storing X 7 as a constant operation Keys Display Description COCDG9C209 7 00 Stores X 7 asa constant operation G 119 00 Multiplies 17 X 7 Qoo 154 00 Multiplies 22 x 7 a09 175 00 Multiplies 25 x 7 Store 519 in register 2 then recall it Cocona 519 00 Stores in register 2 0 00 Clears display 519 00 Recalls register 2 Ata Glance 13 Time Value of Money TVM At a Glance Interest per year Present value Payment Future value Begin or End mode Number of payments Enter any four of the five values and solve for the fifth A negative sign in the display represents money paid out money received is positive Number of payments per year mode If you borrow 14 000 PV for 360 months N at 10 interest I YR
12. OO0B 4 000 00 Enters next cash flow GXDGX9eGOQQG 11 765 29 Enters final cash flow Qe 38 98 Calculates annual nominal yield COGO 3 25 Monthly yield 76 6 Cash Flow Calculations NPV and IRR YR Discontinuing Cash Flows Chapter 4 demonstrates the use of cash flow diagrams to clarify financial problems This section describes discounted cash flows The NPV and IRR YR functions are frequently referred to as discounted cash flow functions When a cash flow is discounted you calculate its present value When multiple cash flows are discounted you calculate the present values and add them together The net present value NPV function finds thc present value of a series of cash flows The annual nominal interest rate must be known to calculate NPV The internal rate of return IRR YR function calculates the annual nominal interest rate that is required to give a net present value of zero The utility of these two financial tools becomes clear after working a few examples The next two sections describe organizing and entering your cash flows Examples of NPV and IRR YR calculations follow Organizing Cash Flows The cash flow series is organized into an initial cash flow CF 0 and succeeding cash flow groups up to 14 cash flows CF 0 occurs at the beginning of the first period A cash flow group consists of a cash flow amount and the number of times it repeats For example in the following cash flow diagram t
13. PMT 930 00 End Mode Set to End mode Press Q 3 if BEGIN annunciator is displayed Keys Display Description CO Oe 12 00 Sets periods per year Go Ce 360 00 Stores the length of the mortgage 30 x 12 9 0 00 Pays mortgage off in 30 years DOCM 7 50 Stores interest rate OQO Ge 930 00 Stores desired pay ment money paid out is negative 133 006 39 Calculates the loan you can afford with a 930 payment 0060005 145 006 39 Adds 12 000 down payment for the total purchase price 5 Time Value of Money Calculations 57 Example A Mortgage With a Balloon Payment You ve obtained a 25 year 172 500 mortgage at 8 8 annual interest You anticipate that you will own the house for four years and then sell it repaying the loan with a balloon payment What will your balloon payment be Solve this problem using two steps 1 Calculate the loan payment using a 25 year term 2 Calculate the remaining balance after 4 years Step 1 First calculate the loan payment using a 25 year term PV 172500 WR 8896 N 25x12 PIYR 12 1 2 DN 299 300 PMT End Mode Set to End mode Press Q 9 if BEGIN annunciator is displayed Keys Display Description OOOH 12 00 Sets periods per year ODOC 300 00 Stores length of mortgage 25 X 12 300 months Ow 0 00 Stores loan balance after 25 years opaan 172 500 00 Stores original loan balance 0Oas 8 80 Stores annual interest Tate 1 424 06 Calculates monthly
14. The second month the same process takes place on the new balance of 1 005 00 The amount of interest paid at the end of the second month is 12 of 1 005 00 or 5 03 The compounding process continues for the third fourth and fifth months The intermediate results in this illustration are rounded to dollars and cents 1 005 00 1 010 03 1 015 08 1 1 020 16 2 102526 3 1 000 00 4 1 005 00 5 1 010 03 1 015 08 1 020 16 The word compound in compound interest comes from the idea that interest previously earned or owed is added to the principal Thus it can earn more interest The financial calculation capabilities of the HP 10BII are based on compound interest 48 4 Picturing Financial Problems Interest Rates When you approach a financial problem it is important to recognize that the interest rate or rate of return can be described in at least three different ways Asa periodic rate This is the rate that is applied to your money from period to period As an annual nominal rate This is the periodic rate multiplied by the number of periods in a year a As an annual effective rate This is an annual rate that considers compounding In the previous example of a 1 000 00 savings account the periodic rate is Y2 per month quoted as an annual nominal rate of 6 2 X 12 This same periodic rate could be quoted as an annual effective rate which considers compounding The balance after 12 months of compounding is
15. also cleared 7 Statistical Calculations 85 Entering Statistical Data There is no limit to the number of values you can accumulate in the statistical registers One Variable Statistics To enter x data for one variable statistics complete the following steps 1 Clear the statistical registers by pressing COLD 2 Enter the first value and press The HP 10BII displays z the number of items accumulated 3 Continue accumulating values by entering the numbers and pressing 9 The z value is incremented with each entry Two Variable Statistics and Weighted Mean To enter x y pairs of statistical data complete these steps 1 Clear the statistical registers by pressing COLD 2 Enter the first x value and press 68 The HP 10BII displays the x value 3 Enter the corresponding y value and press The HP 10BII displays the number of pairs of items accumulated 4 Continue entering x y pairs The z value is incremented with each entry To enter data for calculating the weighted mean enter each data value as x and its corresponding weight as y If statistical data causes the value of a register to exceed 49 99999999999 x 10 the HP 10BII displays a temporary overflow warning OFLO 86 7 Statistical Calculations Correcting Statistical Data Incorrect entries can be deleted using CX If either value of an xy pair is incorrect you must delete and reenter both values Correcting One Variable
16. p Enters amount in group 1 GOV ni Enters number of 2 00 times payment occurs QOOOOBA A O0 m Enters amount in d group 2 GOV n2 Enters number of 3 00 times payment occurs n3 Enters number of 9 00 times payment occurs GXSXoXoene CF4 Enters cash flow group 7 500 00 4 OOOH 5o Enters number of times payment occurs 8 Additional Examples 115 QOOOG OOaa ony Qe oan 116 8 Additional Examples CF6 2 000 00 8 80 29 203 14 24 00 0 00 34 800 58 Enters cash flow group 6 Stores annual interest rate Calculates net present value NPV automatically stored as PV Stores known values Calculates net future value A Assistance Batteries and Service Hewlett Packard is committed to providing you with ongoing support You can obtain answers to questions about using your calculator from our Calculator Support department Please read Answers to Common Questions before contacting us Our experience has shown that many of our customers have similar questions about our products If you don t find an answer to your question you can contact us using the address or phone number listed on the inside back cover Answers to Common Questions Q I m not sure if the calculator is malfunctioning or if I m doing something incorrectly How can I determine if the calculator is operating properly A See Determining if the Calculator Requires Service on page 121 Q My num
17. payment 58 5 Time Value of Money Calculations Step 2 Since the payment is at the end of the month the past payment and the balloon payment occur at the same time The final payment is the sum of PMT and FV PV 172 500 00 VYR 8 896 N 4x12 PAR 12 ae ape 46 47 48 PMT 1 424 06 End Mode FV The value in PMT should always be rounded to two decimal places when calculating FV or PV to avoid small accumulative discrepancies between non rounded numbers and actual dollars and cents payments If the display is not set to two decimal places press Q0 2 Display Description 1 424 06 Rounds payment to two decimal places then stores o 48 00 Stores 4 year term 12 4 that you expect to own house 163 388 39 Calculates loan bal ance after 4 years emo 164 812 45 Calculates total 48 payment PMT and FV to pay off loan money paid out is negative 5 Time Value of Money Calculations 59 Savings Calculations Example A Savings Account If you deposit 2 000 in a savings account that pays 7 2 annual interest compounded annually and make no other deposits to the account how long will it take for the account to grow to 3 000 fV 300000 VYR 7 296 N PAR 1 1 23g 2d Ne PMT 0 PV 2 000 00 Since this account has no regular payments PMT 0 the payment mode End or Begin is irrelevant Keys Display Description Qe 0 00 Clears all registers Cope 1 00 Sets P
18. 1 250 00 to show repayment amount t JJ Calculate the percent change between two numbers m and wOOGO 72 expressed as a percent of m by entering 7 na then press QED lOG66c0 Example Calculate the percent change between 291 7 and DQOOOD 316 8 Keys Display GX9xv ode 291 70 OOQOOSES 8 60 Description Enters m Calculates percent change Example Calculate the percent change between 12 X 5 and 65 18 Keys Display COD Dee 60 00 OSOOSES 3833 34 2 Business Percentages Description Calculates and enters 74 Calculates percent change Margin and Markup Calculations The HP 10BII can calculate cost selling price margin or markup Application Margin Description Margin is markup expressed as a percent of price GS RO MU Markup calculations are expressed as a percent of cost Markup To see any value used by the Margin and Markup application press and then the key you wish to see For example to sec the value stored as S7 press CDC Margin and Markup share the same storage register For example if you store 20 in B then press GDGV you will see 20 00 displayed Margin Calculations Example Kilowatt Electronics purchases televisions for 255 The televisions are sold for 300 What is the margin Keys Display Description Ooew 255 00 Stores cost in CST aoar 300 00 Stores selling price in PRC AR 15 00 Calculates margin Markup
19. 122 86 Berekent de oorspronkelijke betaling 7 Bereken de jaarlijkse effectieve rente van een nominale rente van 10 die maandelijks samengesteld wordt Toetsen Display Beschrijving MOC 10 00 Voert de nominale rente in COE 12 00 Voert het aantal betalingen per jaar in er 10 47 Berekent de jaarlijkse effectieve rente IRR YR en NPV Aantal periodes per jaar standaardwaarde is 12 Cashflows maximaal 15 j geeft het nummer van de cashflowgroep aan C Aantal keren dat cashflow j achtereenvolgens voorkomt qu Inter rendement per jaar Qe Netto huidige waarde Zie voorbeeld op pagina 11 Amortisatie Na het berekenen van een betaling met Time Value of Money TVM voert u de periodes in waarin geamortiseerd wordt en drukt u vervolgens op Druk dan op om de rente hoofdsom en saldowaarden te bekijken respectievelijk aangeduid door de PRIN INT en BAL indicator Amortiseer met behulp van het vorige TVM voorbeeld pagina 6 een enkelvoudige betaling en vervolgens een reeks betalingen Amortiseer de 20 betaling van de lening Toetsen Display Beschrijving aow 20 00 Voert de betaling in die moet geam ortiseerd worden m een 20 20 Geeft de betaling wccr dic moet geamortiseerd worden G 7 25 Geeft de hoofdsom weer 115 601 Geeft de rente weer Betaalde bedragen zijn is negatief 13 865 83 Gccft hct saldo weer Zie voorbeeld op pagina 9 8 Wat is de RR YR als u
20. 28 000 Keys Display Description qoe 28 000 00 Changes initial cash flow 12 49 Calculates annual nominal yield More examples that use NPV and IRR YR calculations are given in chapter 8 Additional Examples 6 Cash Flow Calculations 83 Automatic Storage of IRR YR and NPV When you calculate NPV the result is stored in PV for your convenience To recall that result press D If you haven t changed the TVM values from the last example using NPV page 82 when you press DEV the result is 27 199 92 When you calculate IRR YR the result is also stored in I YR For the previous example press O to display the annualized yield 12 49 84 6 Cash Flow Calculations Statistical Calculations The and QE keys are used to enter and delete data for one and two variable statistics Summation data is stored in memory The labels above the 4 to 9 keys indicate what summation data is stored Once you enter the data you can use the statistical functions to calculate the following Mean and standard deviation m Lincar regression statistics Linear estimation and forecasting m Weighted mean m Summation statistics z Zx o2 Ly Dy and Lay Clearing Statistical Data Clear the statistical registers before entering new data If you don t clear the registers data currently stored is automatically included in the summation calculations To clear the statistical registers press CQ UD The display is
21. 84 Automatic Storage of IRR YR and NPV 85 Statistical Calculations 85 Clearing Statistical Data 86 Entering Statistical Data 86 One Variable Statistics 86 Two Variable Statistics and Weighted Mean 87 Correcting Statistical Data 87 Correcting One Variable Data 87 Correcting Two Variable Data 87 Summary of Statistical Calculations 88 Mean Standard Deviations and Summation Statistics 90 Linear Regression and Estimation 93 Weighted Mean Contents 7 Additional Examples 95 Business Applications 95 Setting a Sales Price 96 Forecasting Based on History 97 Cost of Not Taking a Cash Discount 98 Loans and Mortgages 98 Simple Annual Interest 98 Continuous Compounding 99 Yield of a Discounted or Premium Mortgage 101 AnnualPercentage Rate for a Loan With Fees 103 Loan With a Partial Odd First Period 104 Automobile Loan 105 Canadian Mortgages 106 Whatif TVM Calculations 108 Savings 108 Saving for College Costs 110 Gains That Go Untaxed Until Withdrawal 112 Value of a Taxable Retirement Account 113 Cash Flow Examples 113 Wrap Around Mortgages 115 Net Future Value A 117 Assistance Batterles and Service 117 Answers to Common Questions 118 Environmental Limits 119 Power and Batteries 119 Low Power Annunciator 119 Battery Specifications 119 Installing Batteries 121 Determining if the Calculator Requires Service 122 Limited One Year Warranty 122 What Is Covered 122 What Is Not Covered 123 Consumer Transactions in the
22. 95 PRIN 26 Principal 67 PV See Present value 72 Q Questions 117 Quick reference 11 R Rate effective 49 72 nominal 49 72 periodic 49 R 35 37 Reciprocal 42 Registers 13 arithmetic in 41 numbered 40 statistics 85 Regression 90 Regulatory Information 125 Remaining amount 45 Reset 121 Residual 45 63 37 39 Roots 42 32 Rounding 32 S Sales price setting 95 Sample standard deviation 87 Savings 60 108 Scientific notation 30 Selling price 35 Separators 31 Service 121 Europe 123 USA 123 other countries 123 SHIFT 26 Shift key 27 Sign changing 24 Simple interest 47 Slope 88 Square root 42 Squares 42 Standard deviation 19 88 population 88 sample 87 amp 3 87 STAT 26 27 Statistics ata glance 19 clearing 19 25 85 entering data 86 estimate 19 estimation 90 forecasting 90 key 27 lincar regression 90 mean 19 87 one variable 86 registers 85 standard deviation 19 87 summation 88 two variable 86 37 Storing 37 Summation statistics 88 28 T Terms and conditions 126 Thousands separator 31 Time Value of Money See TVM Troubleshooting 121 Turn off 23 Turn on 23 TVM 53 ata glance 14 15 equations 132 problems 49 TVM 26 Two variable statistics 86 U Uneven cash flow 80 w Warranty 122 Weighted mean 86 93 Wrap around mortgages 113 X 42 Y B43 Yield 83 y intercept 88 Index 143 HP 10BII Business Calculator QUICK REFERENCE GUIDE UJ
23. Calculate the first option Keys Display COO 12 00 Oo 36 00 COGOGXOXQe 12 500 00 QE 0 00 GC 3 50 aD 366 28 ECS 13 185 94 104 8 Additional Examples Description Sets payments per year Stores known values Stores first interest rate Calculates payment Calculates total interest and principal Calculate the second option Keys Display Description DOGO 11 500 00 Stores loan amount with rebate GG 9 50 Stores second interest rate 368 38 Calculates payment Qv 13 261 64 Calculates total interest and principal The first option costs slightly less Canadian Mortgages In Canadian mortgages the compounding and payment periods are not the same Interest is compounded semi annually while payments are made monthly To use the TVM application in the HP 10BII you need to calculate a Canadian mortgage factor which is an adjusted interest rate to store in I YR For additional information on interest rate conversions sce Interest Rate Conversions on page 72 Example What is the monthly payment required to fully amortize a 30 year 130 000 Canadian mortgage if the annual interest rate is 12 Keys Display Description 1 12 00 Stores known nominal Gag E io percentage and number of compounding periods SED 12 36 Calculates annual effective rate O Amc 12 00 Sets payments per year OCGA 11 71 Calculates Canadian mortgage factor adjusted interest rate OOTO 130 000 Stores other
24. M CDE and AD Pressing RD QE recalls the total number of payments in years and shows you the number of payments per year Recalling these numbers does not change the content of the registers Clearing TVM Press QE to clear the TVM registers This sets N I YR PV PMT and FV to zero and briefly displays the current value in P YR 54 Time Value of Money Calculations Begin and End Modes L 4 Before you start a TVM calculation identify whether the Socom first periodic payment occurs at the beginning or end of Eel the first period If the first payment occurs at the end of IOOOOO the first period set your HP 10BII to End mode if it IOOGOO occurs at the beginning of the first period set your ce calculator to Begin mode To switch between modes press QE The BEGIN annunciator is displayed when your calculator is in Begin mode No annunciator is displayed when you are in End mode Mortgages and loans typically use End mode Leases and savings plans typically use Begin mode Loan Calculations Example A Car Loan You are financing a new car with a three year loan at 10 5 annual nominal interest compounded monthly The price of the car is 14 500 Your down payment is 1 500 Part 1 What are your monthly payments at 10 5 interest Assume your payments start one month after the purchase or at the end of the first period PV 14500 1500 WR 1053 Ne3x12 PAR 12 1 2 kcu 35 36 PMT
25. M register press followed by 9 Keys Description C Stores displayed number in the M register Recalls number from the M register Adds displayed number to the M register Example Use the M register to add 17 14 25 and 16 95 Then subtract 4 65 and recall the result Keys Display Description One 17 00 Stores 17 in M register Geo 1425 Adds 14 25 to M register Qe 16 95 Adds 16 95 to M register GX9 Xeno 4 65 Adds 4 65 to M register 43 55 Recalls contents of the M register 3 Number Storage and Arithmetic 39 Using Numbered Registers The and GG keys access the 10 user registers The OST key is used to copy the displayed number to a designated register The key is used to copy a number from a register to the display To store or recall a number in two steps 1 Press or To cancel this step press or 2 Enter the register number 0 through 9 Tn the following example two storage registers are used Calculate the following 415 6 560 1 475 6 3915 S 3915 Keys Display Description OOOOSDD 475 60 Stores 475 60 dis played number in Ry QGOQDVDOSMD 39 15 Stores 39 15 in Ro G 12 15 Completes first calculation GXeXOCXCDGX QD 475 60 Recalls Ry 2 39 15 Recalls Rp e 26 45 Completes second calculation With the exception of statistics you can also use and for application registers For example 61 8 stores the number fr
26. MasterCard to cover the standard repair charge Note that credit cards may not be accepted in Europe Visit http www hp com calculators for more information Ship the calculator in adequate protective packaging to prevent damage Such damage is not covered by the warranty so we recommend that you insure the shipment Pay the shipping charges for delivery to the Corvallis Service Center whether or not the calculator is under warranty Warranty on Service Service is warranted against defects in materials and workmanship for 90 days from the date of service or your original warranty whichever is longer 124 A Assistance Batteries and Service Service Agreements In the US a support agreement is available for repair and service Refer to the form in the front of the manual For additional information contact a HP Service Center see the inside of the back cover Regulatory Information U S A This device complies with Part 15 of the FCC Rules Operation is subject to the following two conditions 1 This device may not cause harmful interference and 2 this device must accept any interference received including interference that may cause undesired operation This calculator generates uses and can radiate radio frequency energy and may interfere with radio and television reception The calculator complies with the limits for a Class B digital device pursuant to Part 15 of the FCC Rules These limits are design
27. Messages Contents 5 Business Percentages 33 Percent Key 33 Finding a Percent 34 Adding or Subtracting a Percent 34 Percent Change 35 Margin and Markup Calculations 35 Margin Calculations 35 Markup on Cost Calculations 36 Using Margin and Markup Together 3 37 Number Storage and Arithmetic 37 Using Stored Numbers in Calculations 37 Using Constants 39 Using the M Register 40 Using Numbered Registers 41 Doing Arithmetic Inside Registers 42 Doing Arithmetic 43 Power Operator 43 Using Parentheses in Calculations 4 45 Picturing Financial Problems 45 How to approach a Financial Problem 46 Signs of Cash Flows 47 Periods and Cash Flows 47 Simple and Compound Interest 47 Simple Interest 48 Compound Interest 49 Interest Rates 49 Two Types of Financial Problems 49 Recognizing a TVM Problem 51 Recognizing a Cash Flow Problem 6 Contents 53 Time Value of Money Calculations 53 Using the TVM Application 54 Clearing TVM 55 Begin and End Modes 55 Loan Calculations 60 Savings Calculations 63 Lease Calculations 67 Amortization 72 Interest Rate Conversions 72 Investments With Different Compounding Periods 73 Compounding and Payment Periods Differ 75 Cash Flow Calculations 75 How to Use the Cash Flow Application 77 NPV and IRR YR Discontinuing Cash Flows 77 Organizing Cash Flows 78 Entering Cash Flows 79 Viewing and Replacing Cash Flows 80 Calculating Net Present Value 83 Calculating Internal Rate of Return
28. amount of annual payment Calculates amount in account at retirement Calculates amount you have paid into account by retirement Calculates interest account has earned by retirement Calculates taxes at 15 of interest Calculates after tax FV Stores after tax future value in FV Calculates present value purchasing power of after tax FV assuming a 4 inflation rate 8 Additional Examples 111 Value of a Taxable Retirement Account This problem uses the TVM application to calculate the future value of a taxable retirement account that receives regular annual payments beginning today Begin mode The annual tax on the interest is paid out of the account Assume the deposits have been taxed already Example If you invest 3 000 each year for 35 years with dividends taxed as ordinary income how much will you have in the account at retirement Assume an annual dividend rate of 8 175 a tax rate of 28 and that payments begin today What is the purchasing power of that amount in today s dollars assuming 4 inflation Set to Begin mode Press QE if BEGIN annunciator is not displayed Keys Display Description Oe 1 00 Sets 1 payment per year QON 35 00 Stores number of payment periods until retirement GXCDCXSO 5 89 Calculates interest rate Gol diminished by tax rate Ge 5 89 Stores adjusted interest rate Ow 0 00 Stores amount you are starting with COCO 3 000 00 Stores amount of annual paymen
29. be and adjust the payment period accordingly 26 compounding periods per year What would be the new term of the loan Cocon Gees QO 3 555 00 26 00 514 82 19 80 Enters new payment Sets payments per year for every two weeks Calculates number of biweekly payments Displays years required to pay off loan Part 3 What if you had monthly payments as in part 1 but chose a 15 year term What would your new payment be What would be the total interest paid on the contract Keys Gea em Gio OOO END EG omo Display 12 00 180 00 8 446 53 1 520 374 70 785 374 70 Description Sets payments per year Stores new term Calculates payment for shorter term Calculates total paid Displays total interest paid on contract 8 Additional Examples 107 Savings Saving for College Costs Suppose you start saving now to accommodate a future series of cash outflows An example of this is saving money for college To determine how much you need to save each period you must know when you ll need the money how much you ll need and at what interest rate you can invest your deposits Example Your oldest daughter will attend college in 12 years and you arc starting a fund for her education She will need 15 000 at the beginning of each year for four years The fund earns 9 annual interest compounded monthly and you plan to make monthly deposits starting at the end of the current mont
30. een initi le uitgaande cashflow hebt van 40 000 gevolgd door maandelijks inkomende cashflows van 4 700 7 000 7 000 en 23 000 Wat is de RR per maand Toetsen Display Beschrijving e 0 00 Wist het hele geheugen een 12 00 Stelt het aantal betalingen per jaar in OOOOBHE 40 000 00 Voert de initi le uitgaande cash tlow in aaO O 4 700 00 Voert de eerste cashflow in OOOOH 7 000 00 Voert de tweede cashflow in GO 2 00 Voert in hoe vaak de cashflow acht ereenvolgens voorkomt DAMMA 23 000 00 Voert de derde cashflow in Qe 15 96 Berekent RR YR ooa 1 33 Berekent RR per maand Wat is de NPY als de discontorente 10 is COQ GYS 10 00 Voert J YR in Or 622 85 Berekent NPV Amortiseer de 15 tot en met de 12 betalingen van de lening DA 12_ Voert de reeks betalingen in die moeten geamortiseerd worden 1 12 Geeft de reeks van periodes betalingen weer G 77 82 Geeft de hoofdsom weer G 1 396 50 Geeft de rente weer Betaalde bedragen zijn negatief 13 922 18 Geeft het saldo weer Rentevoetconversies Om te converteren tussen de nominale en effectieve rente voert u de bekende rente en het aantal periodes per jaar in en berekent u vervolgens de onbekende rente Qeon Nominaal rentepercentage em Effectief rentepercentage OG Periodes per jaar Zie voorbeeld op pagina 10 9 Statistiek man Wist statistische registers getal Voert statistische gegevens met n varia bele in geta
31. initial cash flow Displays cash flow group number for as long as you hold down Oe 0 00 Enters first cash flow group amount GO 6 00 Enters number of repetitions OO0 1 000 00 Enters second cash flow group amount GOV 3 00 Enters number of repetitions OOGo0mM 10 000 00 Enters final cash flow Qu 21 22 Calculates annual nominal yield Viewing and Replacing Cash Flows To view a cash flow press to to display cash flows 0 to 9 or G GOO to 3 to display cash flows 10 to 14 to display the next cash flow RO to display the previous cash flow m OAOE to display the current cash flow 6 Cash Flow Calculations 79 To replace a cash flow amount press to to store the new amount in cash flows 0 to 9 MAOA to to store the new amount in cash flows 10 to 14 a GOGH to store the amount in the next cash flow ri to store thc amount in the previous cash flow GIO JE to store the amount in the current cash flow To replace the number of times a particular cash flow occurs the cash flow whose number of occurrences will change Then enter the number of times it occurs and press CO Since cash flows cannot be deleted or inserted use QED to start over Calculating Net Present Value The net present value NPV function is used to discount all cash flows to the front of the time line using an annual nominal interest rate that you supply These steps describe how to calculate NPV 1 Press QE and store the nu
32. initial cash outflow of 40 000 followed by monthly cash inflows of 4 700 7 000 7 000 and 23 000 what is the IRR YR What is the IRR per month Keys Display Description Qe 0 00 Clears all memory Dacw 12 00 Sets payments per year OOODBHA 40 000 00 Enters initial outflow XXX 4 700 00 Enters first cash flow OOO 7 000 00 Enters second cash flow GOV 2 00 Enters number of consec utive times cash flow occurs GXGX9X9oX9 65 23 000 00 Enters third cash flow Qe 15 96 Calculates IRR YR eS 1 33 Calculates IRR per month What is the NPV if the discount rate is 10 COGO 10 00 Enters I YR Qe 622 85 Calculates NPV 18 Ata Glance Statistics At a Glance Clear statistical registers number Enter one variable statistical data number OE Delete one variable statistical data number 663 number2 Enter two variable statistical data number number QE Delete two variable statistical data Ce Means of x and y Qi Mean of x weighted by j QS Sample standard deviations of x and y Qe Population standard deviations of x and x value Estimate of x and correlation coefficient x value Cai Estimate of x Dev intercept and slope Using the following data find the means of x and y the sample standard deviations of x and y and the y intercept and the slope of the linear regression forecast line Then use summation statistics to find and Ex N x data 4 6 y data 50 90 160 Ata Glanc
33. known values OM DOCH 360 00 for mortgage END 1 308 30 Calculates monthly payment for Canadian mortgage 8 Additional Examples 105 What if TVM Calculations One of the most valuable aspects of the HP 10BII s TVM application is the ease with which it handles the question what if in financial calculations For example one of the most popular what if questions is What if the interest rate changes to How will that affect my payment To answer this question once you have calculated a payment based on one interest rate all you nced to do is enter the new interest rate and recalculate PMT Some of the examples earlier in this manual have included some brief encounters with what if questions but a more complete example follows Example You are about to sign on the dotted line for a 30 year 735 000 mortgage on a vacation home The annual interest rate is 11 2 Part 1 What will your payments be at the end of the month Set to End mode Press QE if BEGIN annunciator is displayed Keys Display Description oHm c 12 00 Sets payments per year MOOOODOH 735 000 00 Stores known values QOOOea 11 20 Goes 360 00 Ow 0 00 ep 7 110 88 Calculates payment 106 8 Additional Examples Part 2 Your company s regular payroll is generated every other Friday The bank agrees to automatically draw payments of 3 555 00 out of each paycheck approximately half of what a monthly payment would
34. memory see below The All Clear message should now be displayed If this is not the case the calculator requires a service Resetting the calculator 1 Turn the calculator over and remove the battery cover 2 Insert the end of a paper clip into the small round hole located between the batteries Insert the clip as far as it will go Hold for one second and then then remove the clip 3 Press Q8 4 If the calculator is still not responding erase the memory sec below and repeat steps 1 to 3 above one more time Erasing the calculator s memory 1 Hold down the key 2 Hold down the 8 and then the V key 3 Release all three keys Memory is cleared and All Clear should be displayed The calculator doesn t respond to keystrokes nothing happens when you press the keys 1 Reset the calculator see above and if necessary 2 erase the memory sce above The All Clear message should now be displayed If this is not the case the calculator requires a service A Assistance Batteries and Service 121 The calculator responds to keystrokes but you suspect that it is malfunctioning 1 It is likely that you ve made a mistake in operating the calculator Try rereading portions of the manual and check Answers to Common Questions on page 117 2 Contact the Calculator Support departmenr The address and phone number are listed on the inside back cover Limited One Year Warranty What Is Covered The
35. on Cost Calculations Example The standard markup on costume jewelry at Kleiner s Kosmetique is 60 They just received a shipment of chokers costing 19 00 each What is the retail price per choker Keys Display Description Oo 19 00 Stores cost Cow 60 00 Stores markup 0 30 40 Calculates retail price 2 Business Percentages 35 Using Margin and Markup Together Example A food cooperative buys cases of canned soup with an invoice cost of 9 60 per case If the co op routinely uses a 15 markup for what price should it sell a case of soup What is the margin Keys Display Description OCO 9 60 Stores invoice cost CGU 15 00 Stores markup RO 11 04 Calculates the price on a case of soup 68 13 04 Calculates margin 36 2 Business Percentages Number Storage and Arithmetic Using Stored Numbers in Calculations You can store numbers for reusc in several different ways m Use X Constant to store a number and its operator for repetitive operations Use 3 Key Memory E32 8 and to store recall and sum numbers with a single keystroke Use and to store to and recall from the 10 numbered registers Using Constants Use to store a number and arithmetic operator for repetitive calculations Once the constant operation is stored enter a number and press The stored operation is performed on the number in the display 3 Number Storage and Arithmetic 37 Keys Operation num
36. standard deviation correlation coefficient and linear regression forecasting plus other statistical calculations Enough memory to store an initial cash flow and 14 cash flow groups with up to 99 cash flows per group Ten numbered storage registers Easy access to functions saves keystrokes and adds convenience Auto increment capability for amortization schedules Labels for amortization and cash flows Automatic constant 3 key memory m Many examples are included in the manual so you can combine them for your specific needs 4 Welcome to the HP 10BII Contents 1i Ata Glance 11 Basics At a Glance 12 Percentages At a Glance 13 Memory Keys At a Glance 14 Time Value of Money TVM At a Glance 15 TVM What if At a Glance 16 Amor zation At a Glance 17 Interest Rate Conversion At a Glance 18 IRR YR and NPV Ata Glance 19 Statistics At a Glance 21 Keyboard Map 1 23 Getting Started 23 Power On and Off 23 Adjusting the Display Contrast 23 Simple Arithmetic Calculations 25 Understanding the Display and Keyboard 25 Cursor 25 Clearing the Calculator 25 Clearing Memory 26 Annunciators 27 Shift Key 27 Statistics Key 28 INPUT Key 28 SWAP Key 28 Math Functions 29 Display Format of Numbers 30 Specifying Displayed Decimal Places 30 Scientific Notation 31 Displaying the Full Precision of Numbers 31 Interchanging the Period and Comma 32 Rounding Numbers 32
37. user terms and conditions HP 10B II Calculator Warranty period 12 months 1 HP warrants to you the end user customer that HP hardware accessories and supplies will be free from defects in materials and workmanship after the date of purchase for the period specified above If HP receives notice of such defects during the warranty period HP will at its option either repair or replace products which prove to be defective Replacement products may be either new or like new 2 HP warrants to you that HP software will not fail to execute its programming instructions after the date of purchase for thc period specified above due to defects in material and workmanship when properly installed and used If HP receives notice of such defects during the warranty period HP will replace software media which does not execute its programming instructions due to such defects 126 A Assistance Batteries and Service 3 HP does not warrant that the operation of HP products will be uninterrupted or error free If HP is unable within a reasonable time to repair or replace any product to a condition as warranted you will be entided to a refund of the purchase price upon prompt return of the product 4 HP products may contain remanufactured parts equivalent to new in performance or may have been subject to incidental use 5 Warranty docs not apply to defects resulting from a improper or inadequate maintenance or calibration b software int
38. 21 Displays INT and the i inter est paid on the 25 pay ment 9 193 28 Displays BAL and the bal ance after the 25 pay ment OO 54 00 Enters payment to amor tize Qe 54 54 Displays PER and the amortized payment period 290 37 Displays PRIN and the principal paid on the 54 payment G 20 05 Displays INT and the inter est paid on the 54 pay ment 1 801 57 Displays BAL and the bal ance after the 54 pay ment eomm 5 Time Value of Money Calculations 71 Interest Rate Conversions The Interest Conversion application uses threc keys Qon OER and QAR They convert between nominal and annual effective interest rates Nominal and effective interest rates are described on pagc 49 If you know an annual nominal interest rate and you wish to solve for the corresponding annual effective rate 1 Enter the nominal rate and press QEA 2 Enter the number of compounding periods and press Q 3 Calculate the effective rate by pressing QEB To calculate a nominal rate from a known effective rate 1 Enter the effective rate and press QER 2 Enter the number of compounding periods and press QC 3 Calculate the nominal rate by pressing O 9 In the TVM application Q 4 and share the same register Interest conversions are used primarily for two types of problems Comparing investments with different compounding periods Solving TVM problems where the payment period and the interest period di
39. 54 BEGIN 26 55 Begin mode 55 Borrowing cquity 113 Buy out valuc 63 c c 25 x 25 Canadian mortgages 105 Capitalized value 63 Cash flow 18 47 diagrams 45 discount 77 entering 78 equations 134 examples 113 initial 77 problems 51 75 84 replacing 79 uneven 80 viewing 79 CF 26 78 C FLOW 26 Chain calculations 24 Clearing display 25 memory 25 messages 25 statistics 85 TVM 54 25 Comma separator 31 117 Compound interest 48 Compounding periods and payment periods 73 different periods 72 Constants 37 Continuous compounding 98 Contrast of display 23 Corrclation coefficient 19 88 140 Index Cost 12 Cost of no discount 97 Gp 35 Cursor 25 D Decimal places 30 Digit separator 31 Discount 97 Discounted mortgage 99 Discounting cash flows 77 639 30 Display contrast 23 Display format 29 Down payment 57 E 30 42 72 Effective interest 17 End mode 55 Environmental limits 118 Equations amortization 132 cash flow calculations 134 interest rate conversions 133 margins and markups 132 statistical 135 TVM 132 Equity 113 ERROR 26 Error messages 137 Estimate 88 Estimation 90 Exponents 30 F Factorial 42 FAQ 117 Forecasting 91 96 Frequently Asked Questions 117 FULL 27 FUNC 27 Functions 28 Future value 45 49 49 G Guarantee 122 Guessing IRR YR 130 Initial cash flow 77 28 INT 26 Interest compound 48 simple 47 Interest conversion at a glance 17 Intere
40. Account You opt for an early retirement after a successful business career You have accumulated a savings of 400 000 that earns an average of 7 annual interest compounded monthly What annuity repctitive uniform withdrawal of funds will you receive at thc beginning of each month if you wish that savings account to support you for the next 50 years PMT 1 2 599 600 FV 0 INR 7 N 600 50 x19 PYR 12 PV 400 000 00 Begin Mode Set to Begin mode Press QEY if annunciator is not displayed 62 5 Time Value of Money Calculations Keys Display Description COO 12 00 Sets payments per year DCCT 400 000 00 Stores your nest egg as an outgoing deposit Oe 7 00 Stores annual interest rate you expect to earn OO 600 00 Stores number of withdrawals Om 0 00 Stores balance of account after 50 years ED 2 392 80 Calculates amount that you can withdraw at the beginning of each month Lease Calculations A lease is a loan of valuable property like real estate automobiles or equipment for a specific amount of time in exchange for regular payments Some leases arc written as purchase agreements with an option to buy at the end of the lease sometimes for as little as 1 00 The defined future value FV of the property at the end of a lease is sometimes called the residual value or buy out value All five TVM application keys can be used in lease calculations There are two common lease calculations
41. Data To delete and reenter statistical data 1 Key in the x value to be deleted 2 Press QE to delete the value The z value is decreased by one 3 Enter the correct value using 29 Correcting Two Variable Data To delete and reenter x y pairs of statistical data 1 Key in the x value press and then key in the y value 2 Press QE to delete the values The z value is decreased by one 5 Enter the correct xy pair using and 9 Summary of Statistical Calculations Some functions return two values The STAT annunciator indicates that two values have been returned Press to see the hidden value Keys Description to Display C Arithmetic mean Mean average of the average of the x values _y values if you entered ydan OB Mean of the x values weighted by the j values Sample standard Sample standard deviation of the x deviation of the y values values if you entered _y data 7 Statistical Calculations 87 Keys Description OS to Display Population standard Population standard deviation of the x deviation of the y values values if you entered y data value OG Estimate of x for a given Corrclation cocfficient t value of y x value Estimate of y fora given Slope m of calculated value of x line 3 J intercept J of the Slope of the calculated line calculated line The sample standard deviation assumes that the data isa sampling
42. HP 10BII Business Calculator Owner s Manual UJ packar Notice For warranty terms and conditions and regulatory information for this calculator see pages 122 to 127 This manual and any examples contained herein are provided as is and are subject to change without notice Hewlett Packard Company makes no warranty of any kind with regard to this manual including but not limited to the implied warranties of merchantability and fitness for a particular purpose Hewlett Packard Company shall not be liable for any errors or for incidental or consequential damages in connection with the furnishing performance or use of this manual or the keystroke programs contained hercin Hewlett Packard Company 2000 All rights reserved Reproduction adaptation or translation of this manual is prohibited without prior written permission of Hewlett Packard Company except as allowed under copyright laws The programs that control your calculator are copyrighted and all rights are reserved Reproduction adaptation or translation of those programs without prior written permission of Hewlett Packard Company is also prohibited Australian Calculator Operation 351 Burwood Highway Forest Hill Victoria 3131 Australia Welcome to the HP 10Bil Your HP 10BII reflects the superior quality and attention to detail in engineering and manufacturing that have distinguished Hewlett Packard products for 60 years Hewlett Packard stands behind this
43. RN EPRN 4 PRN new old Interest Rate Conversions P YR EFF G 4 OAM w 1 x 100 100 x P Y x B More About Calculations 133 Cash Flow Calculations i periodic interest rate J the group number of the cash flow CF amount of the cash flow for group j nj number of times the cash flow occurs for group j amp the group number of the last group of cash flows Nj X n total number of cash flows prior to group j Ist lt j 1 k NPV CF X CF x x 1 22 eie i When NPV 0 the solution for 7 is the periodic internal rate of return 134 B More About Calculations Statistics _ Dey n Xxy oF Ber _ _ zr Gar b j mk amp rb mx b B More About Calculations 135 Page 136 is blank Messages Press or to clear a message from the display All Clear Memory has been erased page 25 COPR HP 2000 Copyright message Interrupted An IRR YR I YR or amortization calculation was interrupted by pressing C No Solution No solution exists for values entered page 129 Not Found s A solution for IRR YR or I YR may or may not exist If you are attempting to solve J YR you may be able to perform the calculation using JRR YR If you are attempting an IRR YR calculation refer to page 129 OFLO Overflow The magnitude of a result is too large for the calculator to handle Message is displayed for a moment then the overfl
44. United Kingdom 8 Contents 123 If the Calculator Requires Service 123 Obtaining Service 124 Service Charge 124 Shipping Instructions 124 Warranty on Service 125 Service Agreements 125 Regulatory Information 126 End user terms and conditions 129 More About Calculations 129 IRR YR Calculations 129 Possible Outcomes of Calculating IRR YR 130 Halting and Restarting IRR YR 130 Entering a Guess for IRR YR 131 Effect of Using Z to Correct Data 131 Range of Numbers 132 Equations 132 Margin and Markup Calculations 132 Time Value of Money TVM 132 Amortization 133 Interest Rate Conversions 134 Cash Flow Calculations 135 Statistics 137 Messages 139 Index Contents 9 Page 10 is blank At a Glance This section is designed for you if you re already familiar with calculator operation or financial concepts You can use it for quick reference The rest of the manual is filled with explanations and examples of the concepts presented in this section Basics At a Glance Keys Display Description 0 00 Turns calculator on Clorange label 0 00 Displays shift annunciator SHIFT eo 0 00 Discontinues shift CX2GG 12 Frases last character 0 00 Clears display OCD 0 00 Clears statistics memory Qe 0 00 Clears all memory Cor Turns calculator off AtaGlance 11 Percentages At a Glance Percent Cost Price Margin Markup Add 1596 to 17 50 Keys Display Description
45. YR to 1 since interest is compounded annually QXoXoXoGDe 2 000 00 Stores amount paid out for first deposit VOLO Ola 3 000 00 Stores the amount you wish to accumulate DOA 7 20 Stores annual interest rate 5 83 Calculates number of years it takes to reach 3 000 60 5 Time Value of Money Calculations Since the calculated value of N is between 5 and 6 it will take six years of annual compounding to achieve a balance of at ast 3 000 Calculate the actual balancc at thc cnd of six years Gg 6 00 Sets to 6 years G3 3 035 28 Calculates amount you can withdraw after 6 years Example An Individual Retirement Account You opened an individual retirement account on April 14 1995 with a deposit of 2 000 80 00 is deducted from your paycheck and you are paid twice a month The account pays 6 3 annual interest compounded semimonthly How much will be in the account on April 14 2010 FP VYR 6 336 N 360 15 years x 24 half months P YR 24 Half months periods DESENE kai PMT 80 00 PV 2 000 00 Set to End mode Press QE if BEGIN annunciator is displayed 5 Time Value of Money Calculations 61 Keys Display Description Ges 24 00 Sets number of periods per year POCO 2 000 00 Stores initial deposit QOwan 80 00 Stores regular semimonthly deposits OTON 6 30 Stores interest rate Gees 360 00 Stores number of deposits GU 52 975 60 Calculates balance Example An Annuity
46. age Rate for a Loan With Fees The annual percentage rate APR incorporates fees usually charged when a mortgage is issued which effectively raises the interest rate The actual amount received by the borrower the PV is reduced while the periodic payments remain the same The APR can be calculated given the term of the mortgage N periods the annual interest rate I PR the mortgage amount new PV and the amount of the fee Remember the cash flow sign convention money paid out is negative money received is positive Example APR for a Loan With Fees A borrower is charged two points for the issuance of a mortgage One point is equal to 1 of the mortgage amount If the mortgage amount is 160 000 for 30 years and the annual interest rate is 8 5 with monthly payments what APR is the borrower paying Set to End Mode Press QE if BEGIN annunciator is displayed Keys Display Description G9 ee a 12 00 Sets payments per year OTET 8 50 Stores interest rate GOCE 360 00 Stores length of mortgage OODDDNH 160 000 00 Stores original amount of mortgage 8 Additional Examples 101 Om 0 00 e 1 230 26 160 000 00 OG 156 800 872 The loan will be completely paid off in 30 years Calculates payment Recalls loan amount Subtracts points Calculates APR considering fees Example Interest Only Loan With Fee A 1 000 000 10 year 12 annual interest interest only loan has an origination fee of three point
47. al line when they occur Where no arrows are drawn no cash flows occur Signs of Cash Flows In cash flow diagrams money invested is shown as negative and money withdrawn is shown as positive Cash flowing ou is negative cash flowing in is positive For example from the lender s perspective cash flows to customers for loans are represented as negative Likewise when a lender receives money from customers cash flows are represented as positive In contrast from the borrower s perspective cash borrowed is positive while cash paid back is negative 46 4 Picturing Financial Problems Periods and Cash Flows In addition to the sign convention cash flowing out is negative cash flowing in is positive on cash flow diagrams there are several more considerations The time line is divided into equal time intervals The most common period is a month but days quarters and annual periods are also common The period is normally defined in a contract and must be known before you can begin calculating m To solve a financial problem with the HP 10BII all cash flows must occur at either the beginning or end of a period m If morc than one cash flow occurs at the same place on the cash flow diagram they are added together or netted For example a negative cash flow of 250 00 and a positive cash flow of 750 00 occurring at the same time on the cash flow diagram are entered as a 500 00 cash flow 750 250 500 m A valid fin
48. ancial transaction must have at least one positive and one negative cash flow Simple and Compound Interest Financial calculations are based on the fact that money earns interest over time There are two types of interest simple interest and compound interest The basis for Time Value of Money and cash flow calculations is compound interest Simple Interest In simple interest contracts interest is a percent of the original principal The interest and principal are due at the end of the contract For example say you loan 500 to a friend for a year and you want to be repaid with 10 simple interest At the end of the year your friend owes you 550 00 50 is 10 of 500 Simple interest calculations are done using the key on your HP 10BII An example of a simple interest calculation is on page 98 4 Picturing Financial Problems 47 Compound Interest A compouad interest contract is like a series of simple interest contracts that are connected The length of each simple interest contract is equal to one compounding period At the end of cach period the interest earned on each simple interest contract is added to the principal For example if you deposit 1 000 00 in a savings account that pays 6 annual interest compounded monthly your earnings for the first month look like a simple interest contract written for 1 month at 1 2 6 12 At the end of the first month the balance of the account is 1 005 00 5 is 2 of 1 000
49. assuming a whole period to be a 30 day month 2 Calculate the payment using the new PV with N equal to the number of full periods Use Begin mode if the number of days until the first payment is less than 30 otherwise use End mode Example A 36 month loan for 4 500 has an annual rate of 15 If the first monthly payment is made in 46 days what is the monthly payment amount assuming 30 day months The odd first period in this example is 16 days Set to End mode Press QES if BEGIN annunciator is displayed Keys Display Description CD es 12 00 Sets payments per year DOT 15 00 Stores interest rate DAA 1 25 Calculates periodic interest rate CD99 09 0 67 Multiplies by fraction of a period DoT 30 00 Calculates amount of simple interest owed for odd period Q O00 4 530 00 Adds this simple interest to present value 8 Additional Examples 103 00N 36 00 Om 0 00 eu 157 03 Automobile Loan Stores term of loan Enters amount left to pay after 36 payments Calculates payment amount Example You are buying a new 14 000 00 sedan Your down payment is 1 500 and you are going to finance the remaining 12 500 The car dealer is offering two choices for financing A 3 year loan with an annual interest rate of 3 5 m A 3 year loan with an annual interest rate of 9 5 and a 1 000 00 rebate With which choice do you pay less for the car Set to End mode Press QE if BEGIN annunciator is displayed
50. ayment 8 Additional Examples 113 Then to calculate the lender s return enter cash flows that represent the complete picture of the wrap around mortgage from the lender s point of view 47 510 22 861 59 82 83 84 180 os 82 510 22 When you group the above cash flows you ll find that CFp 47 510 22 82 510 22 35 000 861 59 754 00 107 59 CF N 82 CF 861 59 N 180 82 98 Keys OCOOR EPISCO GO oam y omea CDGXooOGO Ce ce 114 8 Additional Examples Display CFO 35 000 00 CF1 107 59 Description Enters 35 000 for loan amount Enters net payment for first 82 months Enters number of times payment occurs Enters net payment for next 98 months Enters number of times payment occurs Calculates annual return Net Future Value The net future value can be calculated by using the TVM keys to slide the net present value NPV forward on the cash flow diagram Example Value of a Fund You have made the following deposits over the past two ycars into a money market fund earning 8 8 What is the current balance of the account 1 2 3 4 5 6 7 8 9 I0 Il 12 13 14 I5 16 17 18 19 20 21 22 23 24 3 000 VYR 8 896 12 000 Current Date Set to End mode Press QE if BEGIN annunciator is displayed Keys Display Description Qe Clears all registers Cl 12 00 Sets payments per year OOQOOGA cro Enters initial cash flow 12 000 00 Ow
51. ayment period complete the following steps 1 Enter the nominal rate and press QE Enter the number of compounding periods in a year and press Q9 9 Solve for the effective rate by pressing QE 2 Enter the number of payment periods in a year and press QE Solve for the adjusted nominal rate by pressing Q 9 Example Monthly Payments Daily Compounding Starting today you make monthly deposits of 25 to an account paying 5 interest compounded daily using a 365 day year What will the balance be in seven years Step 1 Calculate the equivalent rate with monthly compounding Keys Display Description Ge 5 00 Stores nominal percentage rate GXe9 m9 365 00 Stores bank s compounding periods per year Qe 5 13 Calculates annual effective rate O Hm CE 12 00 Stores monthly periods Qe 5 01 Calculates equivalent nominal percentage rate for monthly compounding Since NOM and I YR share the same register this value is ready for use in the rest of the problem Step 2 Calculate the future value Set to Begin mode Press Q 29 if annunciator is not displayed 0 00 Stores present value onw 25 00 Stores payment Ges 84 00 Stores total number of payments C 2 519 61 Calculates balance after 7 years 74 5 Time Value of Money Calculations Cash Flow Calculations How to Use the Cash Flow Application The cash flow application is used to solve problems where cash flows occur over regular intervals but arc of
52. balance Payment amount rounded to the display format Number of payments per year The numbers displayed for interest principal and balance are rounded to the current display sctting To Amortize To amortize a single payment enter the period number and press QQ acs The HP 10BII displays the annunciator PER followed by the starting and ending payments that will be amortized Press to see interest INT Press again to see the principal PRIN and again to see the balance BAL Continue pressing to cycle through the same values again To amortize a range of payments enter starting period number 683 ending period number then press QE The HP 10BII displays the annunciator PER followed by the starting and ending payments that will be amortized Then press repeatedly to cycle through interest principal and balance Press again to move to the next set of periods This auto increment feature saves you the keystrokes of entering the new starting and ending periods If you store recall or perform any other calculations during amortization pressing 5 will no longer cycle through interest principal and balance To resume amortization with the same sct of periods press Oe Example Amortizing a Range of Payments Calculate the first two years of the annual amortization schedule for a 30 year 180 000 mortgage at 7 75 annual interest with monthly payments Set to End mode Press QE if BEGIN annunciator i
53. ber OO Stores number as constant Ouunber OO Stores number as constant number OO Stores X number as constant Orumber OO Stores number as constant OBx value OO Stores ye as constant Orumber QOG Stores number as constant Onmber QOG Stores number Yo as constant Q9 number OGO Stores X number as constant Onmber QO Stores number Vo as constant Example Calculate 5 2 6 2 and 7 2 Keys Display Description Gee 2 00 Stores 2 as constant o 7 00 Adds 5 2 GG 8 00 Adds 6 2 GG 9 00 Adds 7 2 Example Calculate 10 10 11 10 and 25 10 Keys Display Description COGO G0 1 00 Stores 10 as constant 11 00 Adds 10 to 10 12 10 Adds 10 to 11 GGG 27 50 Adds 10 to 25 Example Calculate 2 and 4 Keys Display Description DX 3 00 Stores y3 as con stant 8 8 00 Calculates 2 38 3 Number Storage and Arithmetic a 64 00 Calculates 43 Using the M Register The C9 88 and Wkeys perform memory operations on a single storage register called the M register In most cases it is unnecessary to clear the M register since 27 replaces the previous contents However you can clear the M register by pressing 0 CW To add a series of numbers to the M register use H to store the first number and to add subsequent numbers To subtract the displayed number from the number in the
54. bers contain commas instead of periods as decimal points How do I restore the periods A Press Q page 31 Q How do I change the number of decimal places that the HP 10BII displays A Press QES and the number of decimal places that you want page 31 A Assistance Batteries and Service 117 Q What does an E in a number for example 2 51E 13 mean A Exponent of ten for example 2 51 x 107 Refer to Scientific Notation on page 30 Q Why do I get a wrong answer or the No Solution message when using TVM A Be sure to enter a value for four of the five TVM values before you solve for the fifth even if one of the values is zero Don t forget to store a zero for EV if you completely pay off a loan Clearing all the registers Q6 3 before entering your known values accomplishes the same thing Check to see that the calculator is in the appropriate payment mode Begin or End mode and that P YR is set correctly Q How can I change the sign of a number in a list of cash flows A You must replace the cash flow entry See Viewing and Replacing Cash Flows on page 79 Q What does PEND in the display mean A An arithmetic operation is pending in progress Q What does INPUT in the display mean A The key has been pressed page 28 Q Why is IRR YR larger than I expected A This is IRR per year To see a periodic IRR divide IRR YR by P YR Environmental Limits To maintain product re
55. calculator we offer expertise to support its use see inside the back cover and worldwide service Hewlett Packard Quality Our calculators are made to excel and to be easy to use This calculator is designed to withstand the drops vibrations pollutants smog ozone temperature extremes and humidity variations that it may encounter in everyday work life The calculator and its manual have been designed and tested for ease of use We added many examples to highlight the varied uses of the calculator Low power electronics and an advanced power management system gives extended battery life The microprocessor has been optimized for fast and reliable computations using 15 digits internally for precise results Extensive research has created a design that has minimized the adverse effects of static electricity a potential cause of malfunctions and data loss in calculators Welcome to the HP 10BIl 3 Features The features of the HP 10BII and the manual reflect the needs and wishes of many customers A large 12 character display An At a Glance section in the manual for quick reference Applications to solve business and financial tasks Time Value of Money Loans savings leases and amortization schedules Interest Conversion Nominal and effective rates Cash Flows Net present value and internal rate of return Business Percentages Percent change markup and margin calculations Statistics Mean
56. calculator except for the batteries or damage caused by the batteries is warranted by Hewlett Packard against defects in materials and workmanship for one year from the date of original purchase YE you sell your unit or give it as a gift the warranty is automatically transferred to the new owner and remains in effect for the original one year period During the warranty period we will repair or at our option replace at no charge a product that proves to be defective provided you return the product shipping prepaid to a Hewlett Packard service center Replacement may be with a newer model of equivalent or better functionality This warranty gives you specific legal rights and you may also have other rights that vary from state to state province to province or country to country What Is Not Covered Batteries and damage caused by the batteries are not covered by the Hewlett Packard warranty Check with the battery manufacturer about battery and battery leakage warranties This warranty does not apply if the product has been damaged by accident or misuse or as the result of service or modification by other than an authorized Hewlett Packard service center No other express warranty is given The repair or replacement of a product is your exclusive remedy Any other implied warranty of merchantability or fitness is limited to the one year duration of this written warranty 122 A Assistance Batteries and Service Some state
57. cimal while you press Qao 9 88 Rounds to two decimal places specified by pressing Q09 Cose 988000000000 Shows rounded stored number Messages The HP 10BII displays messages about the status of the calculator or informs you that you have attempted an incorrect operation To clear a message from the display press C or Sce Messages on page 137 for a list of meanings 32 1 Getting Started Business Percentages You can use the HP 10BII to calculate simple percent percent change cost price margin and markup Percent Key The key has two functions finding a percent and adding or subtracting a percent Finding a Percent The key divides a number by 100 unless it is preceded by an addition or subtraction sign Example Find 25 of 200 Keys Display Description OO8 200 00 Enters 200 000 0 25 Converts 25 to a decimal 50 00 Multiplies 200 by 25 2 Business Percentages 33 Adding or Subtracting a Percent You can add or subtract a percent in one calculation Example Decrease 200 by 25 Keys Display a000 200 00 a00 50 00 150 00 Description Enters 200 Multiplies 200 by 0 25 Subtracts 50 from 200 Example You borrow 1 250 from a relative and you agree to repay the loan in a year with 7 simple interest How much money will you owe Keys Display OOQSOH 8750 G 1 337 50 Percent Change Description Calculates loan interest Adds 87 50 and
58. e 19 Keys me Gee X99 Gee 9XoG OMDOO H C Ce Qe Omz ose eo eo 20 Ata Glance Display 0 00 1 00 2 00 3 00 4 00 100 00 2 00 55 68 10 00 27 50 3 00 1 420 00 Description Clears statistics registers Enters first x y pair Enters second x y pair Enters third x y pair Displays mean of x Displays mean of y Displays sample stan dard deviation of x Displays sample stan dard deviation of y Displays y intercept of regression line pre dicted y value for x 0 Displays slope of regression line Displays z number of data points entered Displays Zxj sum of the products of x and J values Keyboard Map 10 T 12 Time value of money page 53 Separate two numbers page 28 Percent page 33 Constant page 37 Store and recall page 40 Change sign page 24 Statistics key page 27 Shift key page 27 Clear display cancel operation page 25 Clear all memory page 25 On page 87 Statistical functions page 87 13 14 15 17 18 19 20 21 n through Xxy statistical summation registers page 88 3 key memory page 39 Backspace page 25 Accumulate statistical data page 86 Cash flows page 75 Business functions margin markup cost price page 35 Interest conversion page 72 Amortization page 67 Annunciator lines page 26 Ata Glance 21 Page 22 is bla
59. e different than for data that was entered originally without having to use QE However the difference will not be serious unless the incorrect data has a very large magnitude compared with the correct values in this case you may want to clear the statistical registers and re enter the data Range of Numbers The largest positive and negative numbers available on the calculator are 9 99999999999 x 10 the smallest positive and negative numbers available ace 1 X 109 Underflow briefly diplays UFLO and then displays zero Refer to the messages OFLO and UFLO in Messages following this appendix B More About Calculations 131 Equations Margin and Markup Calculations PRC COS PRC PRC COS cost 1 MAR x 100 mu Time Value of Money TVM Payment Mode Factor S 0 for End mode 1 for Begin mode pu HYR PIYR 1 1 my 100 100 0 Pv v XS x purx 100 N Fvx t 22 100 Amortization EINT accumulated interest ZPRN accumulated principal i periodic interest rate BAL is initially PV rounded to the current display setting PMT is initially PMT rounded to the current display setting i2 I YR P YRx 100 132 B More About Calculations For each payment amortized INT _ BAL X i INT is rounded to the current display setting INT z 0 for period 0 in Begin mode INT INT with sign of PMT PRN PMT INT BAL BAL yg PRN EINT XINT INT EP
60. ed to provide reasonable protection against harmful interference in a residential installation However there is no guarantee that interference will not occur in a particular installation In the unlikely event that there is interference to radio or television reception which can be determined by turning the calculator off and on the user is encouraged to try to correct the interference by one or more of the following measures m Reorient or relocate the receiving antenna Relocate the calculator with respect to the receiver Pursuant to Part 15 21 of the FCC Rules any changes or modifications to this equipment not expressly approved by Hewlett Packard company may void the user s authority to operate this equipment Canada This Class B digital apparatus complies with Canadian EMC Class B requirements Cet appareil num rique de la classe B est comforme la classe B des normes canadiennes de compatibilit lectromagn tiques CEM A Assistance Batteries and Service 125 Japan CORRS MABAESRAMRAEMHGMS VCCI ORK lt SS lt KOMABRHSECT COMMS RERRCHAT SOLE BHELTWETA CORES LFF LEY 3 VR MIELE Han c RHREESIEET TTCA BUST WiRB EI 0E o TELURMYRUELTEFEU Netherlands Batteries are delivered with this product When empty do not throw them away but collect them as small chemical waste Bij dit produkt zijn betterijen geleverd Wanneer deze leeg zijn moet u ze niet weggooien maar inleverenals KCA End
61. en press and hold down both S and FU When you release all three all memory is cleared The All Clear message is displayed 1 Getting Started 25 Annunciators Annunciators are symbols in the display that indicate the status of the calculator Annunciator Status SHIFT STATS PEND BEGIN INPUT AMORT BAL INT PRIN PER C FLOW CF ERROR TVM The shift key G2 has been pressed When another key is pressed the function labeled in orange on the key is executed The statistics key is active When another key is pressed the function labeled in mauve above the key is executed An operation is waiting for another operand Begin mode is active page 55 that is pay ments are at the beginning of a period The 9 key has been pressed and a number stored Battery power is low page 119 The amortization annunciator is lit together with one of the following four annunciators The balance of an amortization is displayed page 68 The interest of an amortization is displayed page 69 The principal of an amortization is displayed page 68 A range of periods for an amortization is used page 68 The cash flow annunciator is lit together with one of the following 2 annunciators The cash flow number appears briefly then the cash flow is shown The cash flow number appears briefly then the number of times the cash flow is repeated is shown The error annunciat
62. ent amounts vary use the procedures described in chapter 6 Cash Flow Calculations m Payments must occur at regular intervals m The payment period must coincide with the interest compounding period If it does not convert the interest rate using the Qoa OEB and keys described on page 72 There must be at least one positive and one negative cash flow 5 Time Value of Money Calculations 53 Key Stores or Calculates a 09e Qe Qe Qe The number of payments or compounding periods The annual nominal interest rate The present value of future cash flows PV is usu ally an initial investment or loan amount and always occurs at the beginning of the first period The amount of periodic payments All payments are equal and none are skipped payments can occur at the beginning or end of each period The future value FV is either a final cash flow or compounded value of a series of previous cash flows FV occurs at the end of the last period Stores the number of periods per year The default is 12 Reset only when you wish to change it This key is located below the GMD key Optional shortcut for storing N Number in display is multiplied by the value in P YR and stores result in N This key is located below the key Switches between Begin and End mode In Begin mode the BEGIN annunciator is displayed Calculates an amortization table To verify values press CO DGD
63. ep GO SCOGX96 36 92 Pressing displays intermediate result 6 9 X 5 35 Ceo 40 57 Completes calculation Chain calculations are interpreted in the order in which they are entered Calculate 4 9 x 3 8 13 00 Adds 4 9 GG 39 00 Mulriplies 13 X 3 Negative Numbers Enter the number and press to change the sign Calculate 75 3 Keys Display Description DOB 75_ Changes the sign of 75 eqeao 25 00 Calculates result 24 1 Getting Started Understanding the Display and Keyboard Cursor The cursor _ is visible when you are entering a number Clearing the Calculator When the cursor is on erases the last digit you entered Otherwise clears the display and cancels the calculation While you are entering a number pressing clears it to zero Otherwise clears the display of its current contents and cancels the current calculation Clearing Messages When the HP 10BII is displaying an error message or clears the message and restores the original contents of the display See Messages on page 137 for a complete list of messages and meanings Clearing Memory Keys Description oc Clears all memory Does not reset modes oa Clears statistical memory Modes on jour HP 1OBIT are number of payments per year page 54 Begin and End page 5 and the display formats page 29 To clear all memory and reset calculator modes press and hold down th
64. erfacing parts or supplies not supplied by HP c unauthorized modification or misuse d operation outside of the published environmental specifications for the product or e improper site preparation or maintenance 6 Hewlett Packard makes no other express warranty or condition whether written or oral To the extent allowed by local law any implied warranty or condition of merchantability satisfactory quality or fitness for a particular purpose is limited to the duration of the express warranty set forth above Some countries states or provinces do not allow limitations on the duration of an implied warranty so the above limitation or exclusion mighr nor apply to you This warranty gives you specific legal rights and you might also have other rights that vary from country to country state to state or province to province 7 To the extent allowed by local law the remedies in this warranty statement are your sole and exclusive remedies Except as indicated above in no event will Hewlett Packard or its suppliers be liable for loss of data or for direct special incidental consequential including lost profit or data or other damage whether based in contract tort or otherwise Some countries States or provinces do not allow the exclusion or limitation of incidental or consequential damages so the above limitation or exclusion may not apply to you 8 For consumer transactions in Australia and New Zealand the warranty terms co
65. ffer Investments With Different Compounding Periods Example Comparing Investments You are considering opening a savings account in one of three banks Which bank has the most favorable interest rate First Bank 6 70 annual interest compounded quarterly Second Bank 6 65 annual interest compounded monthly Third Bank 6 63 annual interest compounded 360 times per year 72 5 Time Value of Money Calculations First Bank Keys Display Description Gone c 6 70 Stores nominal rate Om 5 4 00 Stores quarterly compounding periods SES 6 87 Calculates annual effective rate Second Bank GXO Ge 6 65 Stores nominal rate Ces 12 00 Stores monthly com pounding periods Qe 6 86 Calculates annual effective rate Third Bank GC 6 63 Stores nominal rate GXeXo De 360 00 Stores compounding periods Qe 6 85 Calculates annual effective rate First Bank offers a slightly better deal since 6 87 is greater than 6 86 and 6 85 Compounding and Payment Periods Differ The TVM application assumes that the compounding periods and the payment periods are the same Some loan installments or savings deposits and withdrawals do not coincide with the bank s compounding periods If the payment period differs from the compounding period adjust the interest rate to match the payment period before solving the problem 5 Time Value of Money Calculations 73 To adjust an interest rate when the compounding period differs from the p
66. h The deposits cease when she begins college How much do you need to deposit each month This problem is solved in two steps First calculate the amount you ll need when she starts college Start with an interest rate conversion because of the monthly compounding 15 000 VYR 996 Year 1 Year 2 Year 3 Year 4 Keys Display Description Set to Begin mode Press QE if BEGIN annunciator is not displayed ees 9 00 Stores annual nominal rate CODD 12 00 Stores number of compounding periods used with this nominal rate Qe 9 38 Calculates annual effective rate 108 8 Additional Examples When compounding occurs only once per year the effective rate and the nominal rate are the same GT 9 38 Stores effective rate as annual rate Set to Begin mode Press QE if BEGIN annunciator is not displayed Oen 1 00 Sets 1 payment per year DSO OO 15 000 00 Stores annual withdrawal GG 4 00 Stores number of withdrawals Ow 0 00 Stores balance at end of four years 52 713 28 Calculates amount required when your daughter starts college Then use that PV as the FV on the following cash flow diagram and calculate the PMT PMT 8 Additional Examples 109 Set to End mode Press QE if BEGIN annunciator is displayed Gv 52 713 28 Stores amount you need Om 0 00 Stores amount you are starting with QOO 12 00 Sets payments per year DOON 144 00 Stores number of deposits Ga 9 00 Stores interest ra
67. h power or 4 0 with the decimal point moved 12 places to the left You can enter this number by pressing Oe 30 1 Getting Started Displaying the Full Precision of Numbers To set your calculator to display numbers as precisely as possible press Q9658Q trailing zeros are not displayed To temporarily view all 12 digits of the number in the display regardless of the current display format setting press and hold The number is displayed as long as you continue holding The decimal point is not shown Start with two decimal places COS Keys Display Description CX9OOG 1 43 Divides Qeseo 142857142857 Displays all 12 digits Interchanging the Period and Comma To switch between the period and comma United States and International display used as the decimal point and digit separator press OC For example one million can be displayed as 1 000 000 00 or 1 000 000 00 1 Getting Started 31 Rounding Numbers The calculator stores and calculates using 12 digit numbers When 12 digit accuracy is not desirable use OE to round the number to the displayed format before using it in a calculation Rounding numbers is useful when you want the actual dollars and cents monthly payment Keys Display Description QOSDGSaSS 9 87654321_ Enters a number with more than two non zero decimal places Cas 9 88 Displays two decimal places omo 987654321000 Displays all digits with out the de
68. he initial cash flow is 11 000 The next group of cash flows consists of six flows of zero each followed by a group of three 1 000 cash flows The final group consists of onc 10 000 cash flow 6 Cash Flow Calculations 77 CF3 10 000 N3 1 CF 2 1 000 N2 3 CFI 0 N1 lt 6 CFO 11 000 Whenever you enter a series of cash flows it is important to account for every period on the cash flow diagram even periods with cash flows of zero Entering Cash Flows The HP 10BII can store an initial cash flow plus 14 additional cash flow groups Each cash flow group can have up to 99 cash flows Enter cash flows using the following steps 1 Press QE to clear the resisters 2 Enter the number of periods per year and press GW 3 Enter the amount of the initial investment then press The j stands for the cash flow number 0 through 14 4 Enter the amount of the next cash flow and press 5 If the amount entered in step 4 occurs more than once consecutively enter the number of times it occurs and press OW 6 Repeat steps 4 and 5 for each and CS until all cash flows have been entered 78 6 Cash Flow Calculations Example Enter the cash flows from the preceding diagram and calculate the IRR YR Then calculate the effective interest rate Assume there are 12 periods per year Keys Display Description Qe 0 00 Clears all registers OC 12 00 Sets 8858 to 12 COCOQXOXOGD E 11 000 00 Enters
69. his rate so that it applies to your payment period In the following example P YR 12 so you have to calculate a new NOM using the interest rate conversion application with P YR equal to 12 98 68 Additional Examples Example You currently have 4 572 80 in an account at Dream World Investments that earns 18 annual interest compounded continuously At the end of cach month you deposit 250 00 in the account What will the balance be after 15 years Keys Display Description TO 0 18 Divides nominal rate by 100 1 20 Raises e to 0 18 power GCDGXGXOX9 19 72 Calculates annual effective rate Qe 19 72 Stores effective rate oac 12 00 Sets payments per year Qon 18 14 Calculates annual nominal rate for a monthly payment period Set to End Mode Press if BEGIN annunciator is displayed OOOe 180 00 Stores number of months aoon 250 00 Stores regular payment DADACA 4 572 80 Stores current balance as a negative value like an initial investment v 297 640 27 Calculates account balance after 15 years of payments with 18 interest compounded continuously Yield of a Discounted or Premium Mortgage The annual yield of a mortgage bought at a discount or premium can be calculated given the original mortgage amount PV interest rate I YR periodic payment PMT balloon payment amount FV and the price paid for the mortgage new PV Remember the cash flow sign convention money paid out is negative
70. ket the lessor expects to recover 7 500 64 5 Time Value of Money Calculations Example Lease With Advance Payments Your company Quick Kit Pole Barns plans to lease a forklift for the warehouse The lease is written fora term of 4 years with monthly payments of 2 400 Payments are due at the beginning of the month with the first and last payments due at the onset of the lease You have an option to buy the forklift for 15 000 at the end of the leasing period If the annual interest rate is 9 what is the capitalized value of the lease Begin Mode PV VYR 9 N 48 PAYR 12 44 45 46 47 48 PMT 2 400 00 48th payment due up front FV 15 000 00 This solution requires four steps 1 Calculate the present value of the 47 monthly payments 4 x 12 1 47 2 Add the value of the additional advance payment 3 Find the present value of the buy option 4 Sum the values calculated in steps 2 and 3 Step 1 Find the present value of the monthly payments Set to Begin mode Press Q 9 if annunciator is not displayed 5 Time Value of Money Calculations 65 Keys Display Coe 12 00 Oo 47 00 GOOD eu 2 400 00 Ow 0 00 Oa 9 00 95 477 55 Description Sets payments per year Stores number of payments Stores monthly payment Stores FV for step 1 Stores interest rate Calculates present value of 47 monthly payments Step 2 Add the additional advance payment to PV Store the answer
71. l G3 Verwijdert statistische gegevens met n variabele getall getal2 Voert statistische gegevens met twee varia belen in etall A getal2 Verwijdert statistische gegevens met twee BO variabelen Gne Gemiddelden van x en y Qe Gemiddelde van x gewogen door y Qe Deu Steekproefstandaarddeviatie voor x en y Qeon Populatiestandaarddeviatie voor x en y y waarde Benadering van x en de correlatieco f m irm fici nt x waarde Og Benadgring van y 0m am Snijpdnt met de y as en de richtingsco amp f fici amp otrichtingsco amp ffici nt
72. l Problems How to approach a Financial Problem The financial vocabulary of the HP 10BII is simplified to apply to all financial fields For example your profession may use the term balance balloon payment residual maturity value or remaining amount to designate a value that the HP 10BII knows as V future value The simplified terminology of the HP 10BII is based on cash flow diagrams Cash flow diagrams are pictures of financial problems that show cash flows over time Drawing a cash flow diagram is the first step to solving a financial problem The following cash flow diagram represents investments in a mutual fund The original investment was 7 000 00 followed by investments of 5 000 00 and 6 000 00 at the end of the third and sixth months At the end of the 11 month 5 000 00 was withdrawn At the end of the 16 month 16 567 20 was withdrawn 4 Picturing Financial Problems 45 16 567 20 Up arrows represent positive cash flows money received 5 000 00 The horizontal line represents time It is divided into regular periods Down arrows represent negative cash flows money paid out 5 000 00 6 000 00 7 000 00 Any cash flow example can be represented by a cash flow diagram As you draw a cash flow diagram identify what is known and unknown about the transaction Time is represented by a horizontal line divided into regular time periods Cash flows arc placed on the horizont
73. l radio station For the past six weeks the manager has kept records of the number of minutes of advertising that were purchased and the sales for that week Week iine dd PUE 3 1 2 1 400 2 1 920 3 3 1 100 4 5 2 265 5 5 2 890 6 4 2 200 What is the y intercept the slope and the correlation coefficient x y P d N es AS 3 000 00 forecasted ye 2 000 00 t m 425 88 Sales in Dotlars 1234 56 7 8 Minutes of Advertising 7 Statistical Calculations 91 Keys Ges COGX9XO GO CDee X29 Gees coCOQ 0G OWOOOOH 2000H Gee 2X2X9X9 8 Ge Qa Display 0 00 1 00 2 00 3 00 4 00 5 00 6 00 376 25 425 88 0 90 Description Clears statistical registers Enters minutes and sales for consecutive weeks Calculates y intercept 4 Displays slope Calculates correlation coefficient Estimate what the level of sales would be if the business purchased 7 or 8 minutes of advertising DOB Gd 3 357 38 3 783 25 Estimates sales if 7 minutes of advertising were purchased Estimates sales if 8 minutes were pur chased How many minutes of advertising should Ali s buy to attain sales of 3 000 OOO Omt 6 16 92 7 Statistical Calculations Estimates minutes of advertising required for 3 000 in sales Weighted Mean The following procedure calculates the weighted mean of data points x4 X X Occurring with weights jj Y2 Tyr
74. l the bill must be paid DISC DAYS is the number of days for which the discount is available Example You receive a bill with the credit terms 2 10 NET 30 What is the cost of not taking the cash discount Keys Display Description OOOLHOODS 72 000 00 Calculates numerator in equation COQODDDODSH 98 00 Parentheses force order of calculation O0SG SDaa 36 73 Calculates as an annual percentage rate cost of not taking discount 8 Additional Examples 97 Loans and Mortgages Simple Annual Interest Example Your good friend needs a loan to start his latest enterprise and has asked you to lend him 450 for 60 days You lend him the money at 10 simple annual interest to be calculated on a 365 day basis How much interest will he owe you in 60 days and what is the total amount owed This equation is used for calculating simple annual interest using a 365 day year INTEREST LOAN AMOUNT x INTEREST x TERM OF LOAN IN DAYS 365 Keys Display Description OOMSOO 0 10 Stores interest GXeXOCGXSXe GG 740 Calculates interest owed QMO 457 40 Calculates total owed Continuous Compounding The equation for calculating an effective rate for continuous compounding is EFF 6M0 _1 x 100 To solve a continuous compounding problem complete these steps 1 Compute the annual effective rate using the above equation 2 Either use this effective rate in your calculations with an annual period P YR 1 or convert t
75. liability you should avoid getting the calculator wet and observe the following temperature and humidity limits Operating temperature 0 to 40 C 32 to 104 F Storage temperature 20 to 65 C 4 to 149 F m Operating and storage humidity 90 relative humidity at 40 C 104 F maximum Noise Declaration In the operator position under normal operation per ISO 7779 LpA lt 70dB 118 A Assistance Batteries and Service Power and Batteries The calculator is powered by two 3 volt lithium button cell batteries When changing batteries use only fresh button cell batteries Both batteries must be changed at the same time Do not use rechargeable batteries Low Power Annunciator When the low battery power annunciator C comes on you should replace the batteries as soon as possible If the battery annunciator is on and the display dims you may lose data The All Clear message is displayed if data is lost due to low power Battery Specifications Your HP calculator requires two fresh CR2032 lithium batteries Installing Batteries 1 Have two fresh CR2032 batteries at hand Only touch the batteries by their edges Wipe each battery with a lint free cloth to remove dirt and oil 2 Make sure the calculator is off Note that you will lose the contents of memory when changing the batteries so write down any data that you have stored and need for later use 3 Turn the calculator over and prise off the batte
76. mD 97 877 55 Cy 97 877 55 Adds additional advance payment Stores result in M register Step 3 Find the present value of the buy option GG 48 00 Oem 0 00 MOOGOOBH 15 000 00 10 479 21 Step 4 Add the results of steps 2 and 3 Display 108 356 77 66 5 Time Value of Money Calculations Stores month when buy option occurs Stores zero payment for this step of solution Stores value to discount Calculates present value of last cash flow Description Calculates present capitalized value of lease Rounding discrepancies are explained on page 59 Amortization Amortization is the process of dividing a payment into the amount that applics to interest and the amount that applies to principal Payments near the beginning of a loan contribute more interest and less principal than payments near the end of a loan TIME The key on the HP 10BII allows you to calculate m The amount applied to interest in a range of payments The amount applied to principal in a range of payments m The ban balance after a specified number of payments are made The function assumes you have just calculated a payment or you have stored the appropriate amortization values in I YR PV FV PMT and P YR 5 Time Value of Money Calculations 67 Annual nominal interest rate Starting balance 33 Ending
77. mber of periods per year in P YR 2 Enter the cash flows using and 3 Store the annual nominal interest rate in J YR and press Q09 Example A Discounted Contract Uneven Cash flows You have an opportunity to purchase a contract with the following cash flows End of Month Amount 4 5 000 00 9 5 000 00 10 5 000 00 15 7 500 00 25 10 000 00 80 6 Cash Flow Calculations How much should you pay for the contract if you wish to yield a yearly rate of 15 on your investment VYR 1596 10 000 5 000 5 000 m 4 910 15 25 Keys Display Description OG 0 00 Clears registers oac 12 00 Sets payments per year O 0 00 Enters initial cash flow of zero The cash flow number is displayed as long as you hold down the key Ow 0 00 Enters first cash flow GOV 3 00 Enters number of occurrences GX9X99X 5 000 00 Enters second cash flow OW 0 00 Enters third cash flow GO 4 00 Enters number of occurrences GXOX9X9 5 000 00 Enters fourth cash flow oO 2 00 Enters number of occurrences OW 0 00 Enters fifth cash flow GO 4 00 Enters number of Occurrences GXSX9X9 7 500 00 Enters sixth cash flow ow 0 00 Enters seventh cash flow 6 Cash Fiow Calculations 81 Keys Display Description GOV 9 00 Enters number of occurrences CD 9X9X9 10 000 00 Enters next cash flow The cash flows that describe your prospective investment are now in the calculator You can press GENO followed by PEND and DOW
78. ng sales manufacturing rates or expenses is reviewing historical trends Once you have historical data the data are fit to a curve that has time on the x axis and quantity on the y axis Example Given the following sales data what are the sales estimates for years six and scven Year Sales 1 10 000 2 11 210 3 13 060 4 16 075 5 20 590 Keys Display Description Qa 0 00 Clears statistics registers OMOODOOHL 1 00 Enters first ycar and sales for that year Q MOOOOOH 200 Enters second year s data O4ODOOOH 3 00 Continues data entry GE XCDGXOCDGG 4 00 OMQOO GOH 5 00 Ge 22 000 50 Estimates sales for year six od 24 605 00 Estimates sales for year seven 96 8 Additional Examples Cost of Not Taking a Cash Discount A cash discount gives a buyer a reduction in price if the payment is made within a specified time period For example 2 10 NET 30 means that the buyer can deduct 2 percent if payment is made within 10 days 1f Payment is not made within 10 days the full amount must be paid by the 30 day You can usc the equation shown below to calculate the cost of failing to take the cash discount The cost is calculated as an annual interest rate charged for delaying payment DISC x 360 x 100 COST __DISC x 360x100 amp 100 DISC x TOTAL DAYS DISC DAYS DISC is the discount percent if the payment is made early TOTAL DAYS is the total number of days unti
79. nk Getting Started Power On and Off J To turn on your HP 10BII press To turn the calculator off press the orange shift key CO then also written C2 Since the calculator has continuous memory turning it off docs not affect the information you have stored To conserve energy the calculator turns itsclf off approximately 10 minutes after you stop using it The calculator uses two lithium batteries If you see the low battery symbol lt in the display replace the batteries Refer to appendix A for more information Adjusting the Display Contrast To change the brightness of the display hold down and then press or 3 Simple Arithmetic Calculations Arithmetic Operators The following examples demonstrate using the arithmetic operators 2 and If you press more than one operator consecutively for example G9 all are ignored except the last one If you make a typing mistake while entering a number press to erase the incorrect digits 1 Getting Started 23 Keys Display Description BEARS 87 18 Adds 24 71 and 62 47 When a calculation has been completed by pressing pressing a number key starts a new calculation MO DGOOAS 240 92 Calculates 19 X 12 68 If you press an operator key after completing a calculation the calculation is continued COCOS 356 42 Completes calculation of 240 92 115 5 You can do chain calculations without using after each st
80. ntained in this statement except to the extent lawfully permitted do not exclude restrict or modify and arc in addition to the mandatory statutory rights applicable to the sale of this product to you A Assistance Batteries and Service 127 Page 128 is blank More About Calculations IRR YR Calculations The calculator determines JRR YR for a set of cash flows using mathematical formulas that search for the answer The process finds a solution by estimating an answer and then using that estimate to do another calculation This is called an iterative process In most cases the calculator finds the desired answer since there is usually only onc solution to the calculation However calculating IRR YR for certain sets of cash flows is morc complex There may be more than one or no mathematical solution to thc problem In these cases the calculator displays a message to help you interpret what has happened Possible Outcomes of Calculating IRR YR These are the possible outcomes of an IRR YR calculation Case 1 The calculator displays a positive answer This is the only positive answer However one or more negative answers may exist m Case 2 The calculator finds a negative answer but a single positive answer also exists It displays Pos Irr Also To see the negative answer press to clear the message To search for the positive answer you must input a guess Refer to Entering a Guess for IRR YR below The
81. numbers when using two number functions or two variable statistics The ev key can also be used to evaluate any pending arithmetic operations in which case the result is the same as pressing Pressing exchanges the following The last two numbers that you entered for instance to change the order of division or subtraction m The results of functions that return two values The x and y values when using statistics Math Functions One Number Functions Math functions involving one number use the number in the display Keys Display Description DOOOSH 945 Calculates square root GOGOGQCOG 0 42 1 2 36 is calculated first D G 3 99 Adds 3 57 and 1 2 36 28 1 Getting Started Two Number Functions When a function requires two numbers the numbers are entered like this number 69 number followed by the operation Pressing 685 cvaluates the current expression and displays the INPUT annunciator For example the following keystrokes calculate the percent change between 17 and 29 Keys Display Description oom 17 00 Enters number1 displays the INPUT annunciator Go 9 Enters number2 Oe 70 59 Calculates the percent change Display Format of Numbers When you turn on the HP 10BII for the first time numbers are displayed with two decimal places and a period as the decimal point The display format controls how many digits appear in the display Tf the result of a calculation is a number con
82. of a larger complete set of dara The jon standard deviation assumes that the data constitutes the entire population T The correlation coefficient is a number in the range 1 through 1 that measures how closely the data fits the calculated line A value of 1 indicates a perfect pote correlation and indicates a perfect negative correlation A value close to zero indicates the line is a poor fit Description Number of data points entered Sum of the x values Sum of the y values Sum of the squares of the x values Sum of the squares of the j values Sum of the products of the x and _y values Mean Standard Deviations and Summation Statistics You can calculate the mean X sample standard deviation S and population standard deviation 0 and summation statistics 1 Zx and Ex of x data For x y data you can also calculate the mean sample standard deviation and population standard deviation of the y data and the summation statistics Ly Ly and Xxx 88 7 Statistical Calculations Example 1 A yacht captain wants to determine how long it takes to change a sail She randomly chooses six members of her crew observes them as they carry out the sail change and records the numbers of minutes required 4 5 4 2 3 25 3 5 3 75 Calculate the mean and sample standard deviation of the times Also calculate the root mean square using the formula Xx n Keys Display Description
83. om the display in the register copies the contents from to the display In most cases it is unnecessary to clear a storage register since storing a number replaces the prcvious contents However you can clear a single register by storing 0 in it To clear all the registers at once press QED 40 3 Number Storage and Arithmetic Doing Arithmetic Inside Registers You can do arithmetic inside storage registers Ro through Ro The result is stored in the register New Number in Register COST register number OSD O register number G9 register number OSTO register number Old contents displayed number Old contents displayed number Old contents X displayed number Old contents displayed number Example Store 45 7 in R5 multiply by 2 5 and store the result in R5 Keys Display Description OODSDD 45 70 Stores 45 7 in Rs Docomo 250 Multiplies 45 7 in R4 by 2 5 and stores result 114 25 in Rs 3 114 25 Displays R5 3 Number Storage and Arithmetic 41 Doing Arithmetic Math functions operate on the number in the display Example Calculate then calculate 20 47 2 1 17 Keys Display Description aom 0 25 Calculates the reciprocal of 4 GGOOGO 447 Calculates 20 amp exooe 51 67 Calculates V20 47 20 Goo 1 21 Calculates 1 17 G 52 88 Completes the calculation Example Calculate natural logarithm e 5 Then calculate 790 4 Keys Di
84. or is lit together with one of the following four annunciators There is a TVM error such as solving for P YR 26 1 Getting Started Annunciator Status Continued FULL More than 15 cash flows have been entered or more than 5 unsolved brackets used STAT Incorrect data used in a statistics calculation or when ERROR is not lit a statistical calculation has been performed FUNC A math error has occurred for example division by zero STAT statistical calculation has been performed Shift Key Most of the HP 10BII keys have a second or shifted function printed in orange on the key The orange shift key QQ is used to access these functions When you press the shift annunciator SHIFT is displayed to indicate that the shifted functions are active To turn the SHIFT annunciator off press again For example press followed by also shown as Q969 to multiply a number in the display by itself Statistics Key The statistics key colored mauve is used to access summary statistics from the statistics memory registers When you press the statistics annunciator STATS is displayed This indicates that you can recall one of six summary statistics with the next keystroke sce page 88 To turn the STATS annunciator off press again For example press followed by to recall the sum of the x values entered 1 Getting Started 27 INPUT Key The key is used to separate two
85. ous Memory Keys Stores a constant operation c Stores a value in the M register memory location Recalls a value from the M register 9 Adds a value to the number stored in the M register CCS Stores a value in a numbered register GO Recalls a value from a numbered register Multiply 17 22 and 25 by 7 storing x 7 as a constant operation Keys Display Description COGDG9CDQO 7 00 Stores x 7 119 00 Multiplies 17 x 7 aea 154 00 Multiplies 22 x 7 200 175 00 Store 519 in register 2 then recall it AT 51900 Stores in register 2 0 00 Clears display o9 519 00 Recalls register 2 Multiplies 25 x 7 Basics Keys Display Description 0 00 Turns calculator on orange label 0 00 Displays shift annunciator SHIFT Q 0 00 Discontinues shift oao 12 Erases last character 0 00 Clears display 9 033 0 00 Clears statistics memory QE 9 00 Clears al memory Cor Turns calculator off Time Value of Money TVM Enter any four of the five values and solve for the fifth A negative sign in the display represents money paid out money received is positive Number of payments Interest per year V Present value Payment Future value Begin or End mode Number of payments per year mode 559898 See example on page 6 Percentages G9 Percent 9S Margin Cost 8 Markup GRO Price Add 15 to 17 50 Keys Display Description TANE 17 50 Enters number oe 20 13 Adds 15
86. ow result is returned 9 99999999999E499 The overflow message is also displayed if an intermediate I VM or cashflow calculation results in an overflow condition Pos Irr Also Positive Internal Rate of Return Also An IRR YR calculation produced a negative solution A positive solution also exists page 129 C Messages 137 running Running A calculation is in process UFLO Underflow An intermediate result in TVM is too small for the HP 10BII to process This message is also briefly displayed if any calculation underflows In this case it is followed by zero 138 C Messages Index Keys not listed here can be found in the alphabetic sections of this index Special Keys 23 23 Q9 23 23 42 p 42 O31 D 24 26 26 23 25 Cy 37 39 en 54 LE 33 629 34 G3 5 88 88 88 Gx 88 E 88 85 85 131 G 88 Sj 87 amp 87 88 B 88 86 A Advance payments 65 Ge 67 AMORT 26 Amortization 67 71 balance 67 equations 132 interest 67 principal 67 range of payments 68 single payment 68 70 Amortization at a glance 16 Annual effective rate 49 Annual nominal rate 49 Annual percentage rate 101 Annualized yield 84 Annuity 62 Annunciators 26 APR 101 Arithmetic 42 Arithmetic operators 23 Average 87 B Backspace 23 BAL 26 Balance of loan 67 Balloon payment 45 58 Basics at a glance 11 Batteries 23 119 installing 119 low power 26 Index 139 E
87. plays population standard deviation for weights y Displays thc total of the y s Linear Regression and Estimation the y intercept Linear regression is a statistical method for estimation and forecasting It is used to find a straight line that best fits a set of xy data There must be at least two different xy pairs The straight line provides a relationship between the x and y variables y mx b where m is the slope and bis Linear Regression Calculate b and r the correlation coefficient as follows 1 Clear the statistical registers by pressing QCD 2 Enter the first x value and press 68 The x value is displayed 3 Enter the corresponding y value and press The HP 10BII displays 1 the number of pairs of items accumulated 4 Continue entering x y pairs The value is incremented with each entry 5 To display P the y intercept press OQA Then press to display 7 the slope of the line 6 Press ENE to display 7 the correlation coefficient 90 7 Statistical Calculations Linear Estimation The straight line calculated by linear regression can be used to estimate a_y value for a given x value or vice versa 1 Enter the x y data using the instructions on page 86 2 Enter the known x value or value To estimate x for the given y enter the j value then press Q 2 a To estimate y for the given x enter the x value then press QO Example Forecasting Ali s Azaleas advertises on a loca
88. r the location of the nearest service center Do not ship the calculator for service without first contacting a Hewlett Packard office Visit http www hp com calculators for a list of support centers in Europe In other countries Contact your Hewlett Packard sales office or dealer or write to an authorized HP service center listed on the inside of the back cover for the location of other service centers A Assistance Batterles and Service 123 Tf local service is unavailable you can ship the calculator to an authorized HP service center for repair All shipping reimportation arrangements and customs costs are your responsibility Service Charge There is a standard repair charge for out of warranty service An authorized HP service center listed on the inside of the back cover can tell you how much this charge is The full charge is subject to the customer s local sales or value added tax wherever applicable Calculator products damaged by accident or misuse are not covered by the fixed service charges In these cases charges are individually determined based on time and material Shipping Instructions If your calculator requires service ship it to the nearest authorized service center or collection point Include your return address and description of the problem m Include proof of purchase date if the warranty has not expired a Include a purchase order check or credit card number plus expiration date VISA or
89. re might also be additional negative answers Case 3 The calculator displays a negative answer and no message This is the only answer Case 4 The calculator displays the message Not Found This indicates that the calculation is very complex It might involve more than onc positive or negative answer or there may be no solution To continue the calculation you must store a guess see below B More About Calculations 129 m Case 5 The calculator displays No Solution There is no answer This situation might be the result of an error such as a mistake in keying in the cash flows A common mistake that results in this message is putting the wrong sign on a cash flow A valid cash flow series for an IRR YR calculation must have at least one positive and one negative cash flow Halting and Restarting IRR YR The search for IRR YR may take a relatively long time You can halt the calculation at any time by pressing the key The message Interrupted is displayed Pressing now displays the current estimate for JRK YR You can resume the calculation by Pressing COSI QQ while the current estimate is displayed in the calculator line This continues the calculation from where it left off a Storing a guess for IRR YR discussed below Entering a Guess for IRR YR To enter a guess key in an estimate of JRR YR and then press SO 69 You can enter a guess for IRR YR at these times Before beginning the calculation A fairly accura
90. ry cover E a Accessing the battery compartment A Assistance Batteries and Service 119 4 Remove both batteries There is a danger of explosion if batteries are incorrectly replaced Warnin 9 Replace only with the samc type of battery or with equivalent batteries as recommended by the manufacturer Dispose of used batteries according to the manufacturer s instructions Do not mutilate puncture or dispose of batteries in fire The batteries can burst or explode releasing hazardous chemicals Do not use new and old batteries together and do not mix batteries of different types 5 Insert the new batteries making sure that the positive sign on each battery is facing outward 6 Replace the battery compartment lid 7 Press G9 Tf the calculator does not turn on follow the procedures in the next section 120 A Assistance Batteries and Service Determining if the Calculator Requires Service Use these guidelines to determine if thc calculator requires service If these procedures confirm that the calculator is not functioning properly read the section If the Calculator Requires Service on page 123 The calculator won t turn on nothing is in the display This condition most likely indicates that the batteries have run out Install new batterics If the calculator still does not turn on when you press 08 1 reset the calculator see below and if necessary 2 erase the
91. s What is the yield to the lender Assume that monthly payments of interest are made Set to End mode Press QE if BEGIN annunciator is displayed Keys Display COS 12 00 OOaa 12 00 OOO 120 00 MOOGDADOD 1 000 000 00 GB 1 000 000 00 em 10 000 00 om 1 000 000 00 OG 970 000 00 G3 12 53 102 8 Additional Examples Description Sets payments per year Stores interest rate Stores length of mortgage Stores original amount of mortgage Enters amount due at end of term Payments are interest only so entire loan amount is due Calculates interest only payments Recalls loan amount Subtracts points Calculates APR Loan With a Partial Odd First Period TVM calculations apply to financial transactions where each payment period is the same length However situations exist where the first payment period is not the same length as the remaining periods This first period is sometimes called an odd or partial first period If interest is applied to an odd first period it is usually calculated as simple interest So using the HP 10BII to do a payment calculation with an odd first period is a two step process 1 Calculate the amount of simple interest that accrues during the fractional first period and add it to the loan amount This is the new PV You must be able to calculate the length of the odd first period as a fraction of the whole period For example a 15 day odd first period would be 0 5 periods
92. s provinces or countries do not allow limitations on how long an implied warranty lasts so the above limitation may not apply to you In no event shall Hewlett Packard Company be liable for consequential damages Some states provinces or countries do not allow the exclusion or limitation of incidental or consequential damages so the above limitation or exclusion may not apply to you Products are sold on the basis of specifications applicable at the time of manufacture Hewlett Packard shall have no obligation to modify or update products once sold Consumer Transactions in the United Kingdom This warranty shall not apply to consumer transactions and shall not affect the statutory rights of a consumer In relation to such transactions the rights and obligations of Seller and Buyer shall be determined by statute If the Calculator Requires Service Hewlett Packard maintains service centers in many countries These centers will repair a calculator or replace it with the same model or one of equal or greater value whether it is under warranty or not There is a service charge for service after the warranty period Calculators normally are serviced and reshipped within five working days Obtaining Service 1 In the United States Send the calculator to an authorized HP service center listed on the inside of the back cover In Europe Contact your Hewlett Packard sales office or dealer or Hewlett Packard s European headquarters fo
93. s displayed 68 5 Time Value of Money Calculations Keys Display Deam c 12 00 Goes 360 00 DODOMA 7 75 CDGXOXOQOXQO 9 180 000 00 Ow 0 00 1 289 54 Description Sets payments per year Stores total numbcr of payments Stores interest per year Stores present value Stores future value Calculates monthly payment If you already know the mortgage payment you can enter and store it just like you store the other four values Next amortize the first year owog 12 Qe 1 12 G 1 579 82 G 13 894 66 178 420 18 Enters starting and ending periods Displays the PER annunciator and range Displays the PRIN annunciator and the principal paid in the first year Displays the INT annunciator and the interest paid in the first year Displays the BAL annunciator and the loan balance after one year The amount paid toward interest and principal 13 894 67 1 579 84 15 474 51 equals the total of 12 monthly payments 12 X 1 289 54 15 474 51 The remaining balance equ als the initial mortgage less the amount applied toward principal 180 000 1 579 84 178 420 16 5 Time Value of Money Calculations 69 Amortize the second year Ce 13 24 1 706 69 G 13 767 79 176 713 49 Displays PER and the next range of periods Displays PRIN and the principal paid in the second year Displays INT and the interest paid in the sec ond year Displays BAL and the loan balance after 24 paymen
94. splay Description QOS 12 18 Calculates e en 2 50 Calculates natural loga rithm of the result GX9eXoXe ao 24 00 Calculates 4 factorial G 814 00 Completes calculation 42 3 Number Storage and Arithmetic Power Operator The power operator C289 raises the preceding number y value to the power of the following number x value Example Calculate 125 then find the cube root of 125 Keys Display Description OAAS 195312500 Calculates 125 DADOAD 5 00 Calculates the cube eX root of 125 or 1251 3 Using Parentheses in Calculations Use parentheses to postpone calculating an intermediate result until you ve entered more numbers You can enter up to four open parentheses in each calculation For example suppose you want to calculate Gi If you enter 39 8 8 O the calculator displays the intermediate result 0 35 This is because calculations without parentheses are performed from left to right as you enter them 3 Number Storage and Arithmetic 43 To delay the division until you ve subtracted 12 from 85 use parentheses Closing parentheses at the end of the expression can be omitted For example entering 25 3 X 9 12 is equivalent to 25 3 X 9 12 Keys Display Description GXOCCXUGSO 8500 No calculation yet oaeo 73 00 Calculates 85 12 0 41 Calculates 30 73 Ge 3 70 Multiplies the result by 9 44 3 Number Storage and Arithmetic Picturing Financia
95. st rate conversion 72 Interest only loan 102 Inverse 42 IRR calculating 83 IRR YR 51 129 at a glance 18 automatic storage of 84 IRR YR calculations entering guesses 130 halting 130 possible outcomes 129 restarting 130 49 e 51 K L 9 37 Lease 63 with advance payments 65 Linear regression 19 90 42 Loans 55 98 interest only 102 numbcr of payments 54 odd first period 103 Logarithm 42 M M register 13 37 39 35 Margin 12 35 Markup 12 35 Maturity value 45 Mean 19 87 88 weighted 86 93 Memory clearing 25 121 Memory keys at a glance 13 Messages 32 137 clearing 25 Mortgages 98 Canadian 105 discounted 99 example of 57 with a balloon payment 58 wrap around 113 35 N 88 49 N 26 42 Natural logarithm 42 Negative numbers 24 Net future value 115 78 os 72 Nominal interest 17 Index 141 NPV 51 at a glance 18 automatic storage of 84 calculating 80 Numbers display format 29 full precision 31 negative 24 range of 131 rounding 32 storing 37 Oo Odd first payment 103 23 23 One variable statistics 86 Operating conditions 118 Operators arithmetic 23 P Parentheses 43 49 Payment advance 65 balloon 58 periods 73 PEND 26 PER 26 Percent 12 adding or subtracting 34 change 34 Percentages 33 at a glance 12 Periodic rate 49 Periods 17 47 49 73 EMD 49 Population standard deviation 88 Powers 43 35 Precision 31 49 142 Index Present valuc 49 Price 12
96. t Ev 345 505 61 Calculates amount in account at retirement Cy a man 87 556 47 Calculates present value purchasing power of FV assuming a 4 inflation rate 112 8 Additional Examples Cash Flow Examples Wrap Around Mortgages wrap around mortgage is a combination of refinancing a mortgage and borrowing against real estate equity Usually the two unknown quantities in the wrapped mortgage arc the new payment and the rate of return to the lender To arrive at a solution you need to use both the TVM and the cash flow applications Example You have 82 monthly payments of 754 left on your 8 mortgage leaving a remaining balance of 47 510 22 You would like to wrap that mortgage and borrow an additional 35 000 for another investment You find a lender who is willing to wrap an 82 510 22 mortgage at 9 5 for 15 years What are your new payments and what return is the lender getting on this wrap around mortgage The payment calculation is a straightforward TVM payment calculation using the new amount as the PV Set to End mode Press QE if BEGIN annunciator is displayed Keys Display Description Qe 0 00 Clears all registers CO Des 12 00 Sets payments per year OBOOODOOGHNV 82 510 22 Stores loan amount on which your new payment is calculated 0Oas 9 50 Stores interest rate Or 0 00 Stores final balance OOO 180 00 Stores number of monthly payments you will make e 861 59 Calculates your new p
97. taining more significant digits than can be displayed in the current display format the number is rounded to fit the current display setting Regardless of the current display format each number is stored internally as a signed 12 digit number with a signed three digit exponent 1 Getting Started 29 Specifying Displayed Decimal Places To specify the number of displayed decimal places 1 Press Q6 2 Enter the number of digits 0 through 9 that you wish to appear after the decimal point Keys Display Description 0 00 Clears display C69 0 000 Displays three decimal places O0O 5 727 CXD 5 727360000 Displays nine decimal places Qos 5 73 Restores two decimal places and rounds number in display When a number is too large or too small to be displayed in DISP format it automatically displays in scientific notation Scientific Notation Scientific notation is used to represent numbers that are too large or too small to fit in the display For example if you enter the number 10 000 000 amp 10 000 000 the result is 1 00E14 which means one times ten to the fourteenth power or 1 00 with the decimal point moved fourteen places to the right You can enter this number by pressing 1E 14 The E stands for exponent of ten Exponents can also be negative for very small numbers The number 0 000000000004 is displayed as 4 00E 12 which means four times ten to the negative twelft
98. te Eu 204 54 Calculates monthly deposit required Gains That Go Untaxed Until Withdrawal You can use the TVM application to calculate the future value of a tax free or tax deferred account Current tax laws and your income determine whether both interest and principal are tax free You can solve for either case The purchasing power of that future value depends upon the inflation rate and the duration of the account Example You arc considering opening a tax deferred account with a dividend rate of 8 175 If you invest 2 000 at the beginning of each year for 35 years how much will be in the account at retirement How much will you have paid into the account How much interest will you have earned If your post retirement tax rate is 15 what will the after tax future value of the account be Assume that only the interest is taxed assume the principal was taxed before deposit What is the purchasing power of that amount in today s dollars assuming a 4 inflation rate 110 8 Additional Examples Set to Begin mode Press QE3 if BEGIN annunciator is not displayed Keys G9 em c ooo Ow DATOE GO EP GRO C Dwm GIC D OOA Display 1 00 35 00 8 18 0 00 2 000 00 387 640 45 70 000 00 317 640 45 47 646 07 339 994 39 339 994 39 86 159 84 Description Sets 1 payment per year Stores number of periods and interest sate Stores amount you start with Stores
99. te guess can reduce the time required to calculate an answer and reduce the chance of the calculator solving for an undesirable negative solution After you ve interrupted the calculation m After the calculator has halted the calculation due to any of the aforementioned cases However for cases 3 and 5 no other solutions will bc found When calculating IRR YR using a guess the calculation halts when it finds an answer However there may be additional positive or negative answers or no true solution at all You can continue searching for another solution by halting the calculation and entering a different guess One way to obtain a good guess for IRR YR is to calculate the NPV for various interest rates Since IRR YR is the interest rate at which NPV equals zero the best estimate of IRR YR is the interest rate that yields the value for NPV closest to zero 130 B More About Calculations Effect of Using to Correct Data The HP 10BII stores the statistical numbers in an accumulated fashion Tt doesn t store every number that you enter but rather it performs intermediate calculations when you press the key The QO key performs the opposite intermediate calculations to effectively remove a number or pair of numbers from the stored results When correcting statistical data QE does not delete rounding errors that may occur during the intermediate calculations done by Thus subsequent results for corrected data may b
100. ts The amount paid toward interest and principal 13 767 79 1 706 69 15 474 51 equals the total of 12 monthly payments 12 X 1 289 54 15 474 51 The remaining balance equals the initial mortgage less the amount applied toward principal 180 000 1 579 84 1 706 69 176 713 49 More money is applied to principal during the second rather than the first year The succeeding years continue in the same fashion Example Amortizing a Single Payment Amortize the 1 25 and 54 payments of a five year car lease The lease amount is 14 250 and the interest rate is 11 5 Payments are monthly and begin immediately Set to Begin mode Press QE if annunciator is not displayed Keys Display CD Oe 12 00 Ges 60 00 COCOS 11 50 COGO 14 250 00 Qv 0 00 310 42 70 5 Time Value of Money Calculations Description Sets payments per year Stores number of payments Stores interest per year Stores present value Stores the future value Calculates monthly payment Amortize the 1 25 and 54 payments 1 00 Enters first payment Displays PER and the amortized payment period 310 42 Displays PRIN and the first principal payment 0 00 Displays INT and the inter est 13 939 58 Displays BAL and the loan balance after one payment pow 25 00 Enters payment to amor tize Qe 25 25 Displays PER and the amortized payment period 220 21 Displays PRIN and the principal paid on the 25 payment G 90
101. us TVM example page 14 amortize a single payment and then a range of payments Amortize the 20 payment of the loan Keys Display Description QOS 20 00 Enters period to amortize Qe 20 20 Displays period to amortize G 7 25 Displays principal 5 115 61 Displays interest Money paid out is negative G 13 865 83 Displays balance Amortize the 1 through 12 loan payments OOO 12_ Enters range of periods to amortize Qe 1 12 Displays range of periods payments 77 82 Displays principal 1 396 50 Displays interest Money paid out is negative 13 922 18 Displays balance 16 Ata Glance Interest Rate Conversion At a Glance Ces Nominal interest percent Qes Effective interest percent Periods per year To convert between nominal and effective interest rates enter the known rate and the number of periods per year then solve for the unknown rate Find the annual effective interest rate of 10 nominal interest compounded monthly Keys Display CO Dor 10 00 Oam 12 00 Ce 10 47 Description Enters nominal rate Enters payments per year Calculates annual effective interest AtaGlance 17 IRR YR and NPV At a Glance Number of periods per year default is 12 Cash flows up to 15 j identifies the cash flow number Number of consecutive times cash flow j occurs Internal rate of return per year Net present value If you have an
102. varying amounts You can also use cash flow calculations to solve problems with regular equal periodic cash flows but these situations are handled more easily using TVM In general these are the steps for cash flow calculations on the HP 10BII 1 Organize your cash flows on paper A cash flow diagram is useful 2 Clear the registers 3 Enter the number of periods per year 4 Enter the amount of the initial investment 5 Enter the amount of the next cash flow 6 If the amount entered in step 5 occurs more than once consecutively enter the number of times it occurs 7 Repeat steps 5 and 6 for each cash flow and group 8 To calculate net present value enter the annual interest rate and press then press COP Or to calculate annual internal rate of return press QE Example A Short Term Investment The following cash flow diagram represents an investment in stock over three months Purchases were made at the beginning of each month and the stock was sold at the end of the third month Calculate the annual internal rate of return and the monthly rate of rcturn 6 Cash Flow Calculations 75 Flows received are positive Flows paid out are negative 4 000 00 5 000 00 Keys Display Description Qe 0 00 Clears all registers OOOH 12 00 Stores periods per year XXe 5 000 00 Enters initial cash flow Displays cash flow group number while you hold down GXoXoXo Ge 2 000 00 Enters next cash flow

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