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HP 10BII

1. TIME gt The x key on the HP 10BI allows you to calculate a The amount applied to zv erest in a range of payments m The amount applied to principal in a range of payments a The oan balance after a specified number of payments are made The Q x 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 38G z 3068 Ending balance PMT Payment amount rounded to the display format OER Number of payments per year The numbers displayed for interest principal and balance are rounded to the current display setting To Amortize To amortize a single payment enter the period number and press Q sor 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 W1 ending period number then press g or The HP 10BII displays the annunciator PER followed by the starting and ending payments that will be amortized Then
2. Q How do I change the number of decimal places that the HP 10BII displays A Press QOS 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 if you completely pay off a loan Clearing all the registers GCA 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 JRR 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 reliability you should avoid getting the calculator wet and observe the following temperature and humidity limi
3. 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 tothe HP 10BIl 3 Features The features of the HP 10BII and the manual reflect the needs and wishes of many customers m A large 12 character display a An At a Glance section in the manual for quick reference m Applications to solve business and financial tasks e Time Value of Money Loans savings leases and amortization schedules e Interest Conversion Nominal and effective rates e Cash Flows Net present value and internal rate of return e Business Percentages Percent change markup and margin calculations e Statistics Mean 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 wit
4. To clear all memory and reset calculator modes press and hold down QN then press and hold down both N and Fv 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 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 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 th
5. Calculates payment Calculates total interest and principal Calculate the second option Keys Display Description DOOOORM 11 500 00 Stores loan amount with rebate OCO 9 50 Stores second interest rate PMT 368 38 Calculates payment ARDANE 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 see 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 ee Stores known nominal percentage and number of compounding periods E 12 36 Calculates annual effective rate ODOQern 12 00 Sets payments per year Ca uo 11 71 Calculates Canadian mortgage factor adjusted interest rate TOTTE 130 000 Stores other known values OMOAOS 360 00 for mousaee PMT 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 eas
6. Year 1 Year 2 Year 3 Year 4 Keys Display Description Set to Begin mode Press QJ 29 if BEGIN annunciator is not displayed Des won 9 00 Stores annual nominal rate OB errr 12 00 Stores number of compounding periods used with this nominal rate a GFF 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 YR 9 38 Stores effective rate as annual rate Set to Begin mode Press QJ 29 if BEGIN annunciator is not displayed Orr 1 00 Sets 1 payment per yeat ODOOOMErm 15 000 00 Stores annual withdrawal OW 4 00 Stores number of withdrawals OV 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 FV from previous I YR 9 calculation 1 2 3 A eo o o PMT 8 Additional Examples 109 Set to End mode Press Qo 9 if BEGIN annunciator is displayed EDEV 52 713 28 Stores amount you need OPV 0 00 Stores amount you are starting with Oe cia 12 00 Sets payments per yeat DDN 144 00 Stores number of deposits Q WYR 9 00 Stores interest rate PMT 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 acc
7. You can do chain calculations without using after each step OOOWHOWOS amp 36 92 Pressing displays intermediate result 6 9 x 5 35 ooe 40 57 Completes calculation Chain calculations are interpreted in the order in which they are entered Calculate 4 9 x 3 ook 13 00 Adds 4 9 OB 39 00 Multiplies 13 x 3 Negative Numbers Enter the number and press to change the sign Calculate 75 3 Keys Display Description 75_ Changes the sign of 75 Slee 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 l 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 C 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 Oar Clears statistical memory Modes on your HP 10BI ate number of payments per year page 54 Begin and End page 55 and the display formats page 29
8. 4 Remove both batteries a There is a danger of explosion if batteries are incorrectly replaced Warnin g Replace only with the same 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 ON If 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 the 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 batteries If the calculator still does not turn on when you press ON 1 reset the calculator see below and if necessary 2 erase the memory see below The All Clear message should now be displayed If this is not the case the calcula
9. 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 m 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 a la classe B des normes canadiennes de compatibilit lectromagn tiques CEM A Assistance Batteries and Service 125 Japan CORRS HRUBRESERBESEMHBMS VCCI OM TES PIMHRRAHSECT COMBS RERACHATAZCLE BRELTWETA CORBAS LAPT LEY aU BIEL TE Asht SMBs EBMOTFCeEMHVET WRR Eo TIEL UY RUE LT FEL Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste Instead it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste
10. SES mT omm Cam O CO 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 value for x 0 Displays slope of regression line Displays number of data points entered Displays Ly sum of the products of x and p values Keyboard Map CPONAaAP ONS 21 6 Re M RM Me 14 b gt xt z i S a A s a E a nae B B B pB n p 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 aos Be DISP n through Lxy 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 li
11. 199 92 7 330 34 6 224 95 1 15 per year 4 415 91 10 000 00 7 500 00 4 471 10 st ae 5 000 00 A J 4 757 62 1 3 5 7 9 W 13 15 17 19 21 23 25 82 6 Cash Flow Calculations Calculating Internal Rate of Return 1 Press QCA store number of periods per year in P YR 2 Enter the cash flows using CF and N 3 Press f 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 RR 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 yield This is an IRR YR calculation that requires a slight modification to the currently stored cash flows 10 000 IRR YR 28 000 Keys Display Description AWOOWOtHE9 28 000 00 Changes initial cash flow CO Ca 9 12 49 Calculates annual nominal yield More examples that use NPV and RR 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 RDEV If you haven t changed the TVM values from the last example using NPV page 82 when you press the result is 27 199 92 When you calculate IRR
12. 60 00 Stores number of payments OLO 11 50 Stores interest per year DoT 14 250 00 Stores present value OE 0 00 Stores the future value PMT 310 42 Calculates monthly p ayment 70 5 Time Value of Money Calculations Amortize the 1 25 and 54 payments INPUT 1 00 Enters first payment an 1 1 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 BOU 25 00 Enters payment to amor tize Cap 0H 25 25 Displays PER and the amortized payment period 220 21 Displays PRIN and the principal paid on the 25th payment G 90 21 Displays INT and the inter est paid on the 25 pay ment 9 193 28 Displays BAL and the bal ance after the 25 pay ment gom 54 00 Enters payment to amor tize ao eon 54 54 Displays PER and the amortized payment period 290 37 Displays PRIN and the principal paid on the 54th payment 20 05 Displays INT and the inter est paid on the 54th pay ment 1 801 57 Displays BAL and the bal ance after the 54 pay ment D D 5 Time Value of Money Calculations 71 Interest Rate Conversions The Interest Conversion application uses three keys i EFF and eY They convert between nominal and annual effective interest rates Nominal and effective interest rates are described on page 49 DOOD If you know
13. CTCE 2 00 Om 8 8 G 3 00 HOOCIMOE 4 00 Z Kw 509 44 Description Clears statistics memoty Enters first rent and its weight Enters second rent and its weight Enters third rent and its weight Enters fourth rent and its weight Calculates weighted mean 7 Statistical Calculations 93 Additional Examples Business Applications Setting a Sales Price One method for setting the per unit sales price 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 DOOWOWOS 40 000 00 Enters cost TMO 20 00 Calculates unit cost SCOM 24 00 Calculates unit sales ODOO price 8 Additional Examples 95 Forecasting Based on History One method of forecasting 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 seven Y
14. 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 A solution for IRR YR or I YR may or may not exist If you are attempting to solve I YR you may be able to perform the calculation using IRR 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 overflow result is returned 9 99999999999E499 The overflow message is also displayed if an intermediate TVM 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 23 23 42 42 31 24 O 26 326 23 25 37 39 54 33 34 88 88 88 88 88 85 85 131 88 87 87 88 88 A Advance payments 65 67 AMORT 26 Amortization 67 71 balance
15. Europe Visit http www hp com calculators for more information m 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 m 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 U S 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 designed to provide reasonable protection against harmful interference in a residential installation
16. Obtaining Service Service Charge Shipping Instructions Warranty on Service Service Agreements Regulatory Information End user terms and conditions More About Calculations IRR YR Calculations Possible Outcomes of Calculating IRR YR Halting and Restarting IRR YR Entering a Guess for IRR YR Effect of Using X to Correct Data Range of Numbers Equations Margin and Markup Calculations Time Value of Money TVM Amortization Interest Rate Conversions Cash Flow Calculations Statistics Messages Index Contents 9 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 amp orange label 0 00 Displays shift annunciator SHIFT 0 00 Discontinues shift oO 12_ Erases last character 0 00 Clears display OCE 0 00 Clears statistics memory ea 0 00 Clears all memory C Turns calculator off At a Glance 11 Percentages At a Glance L J m Tt JB CoO 55 Percent Cost Price MARJ Margin Markup Add 15 to 17 50 Keys Display Description ODOOOW 17 50 Enters number TOE 20 13 Adds 15 Find the margin if the cost is 15 00 and selling price is 22 00 CST 15 00 Enters cost PRO 22 0
17. Variable Statistics and Weighted Mean To enter x y pairs of statistical data complete these steps 1 Clear the statistical registers by pressing QJCLY 2 Enter the first x value and press 4 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 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 Tf statistical data causes the value of a register to exceed 9 99999999999 x 10199 the HP 10BII displays a temporary overflow warning OFLO 86 7 Statistical Calculations Correcting Statistical Data Incorrect entries can be deleted using QJ If either value of an x y pair is incorrect you must delete and reenter both values Correcting One Variable Data To delete and reenter statistical data 1 Key in the x value to be deleted 2 Press G5 to delete the value The value is decreased by one 3 Enter the correct value using 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 25 to delete the values The v value is decreased by one 3 Enter the correct x y pair using and z Summary of Statistical Calculations Some functions return two values The STAT annunciator indicates
18. YR the result is also stored in I YR For the previous example press to display the annualized yield 12 49 84 6 Cash Flow Calculations Statistical Calculations The and QJG 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 keys indicate what summation data is stored Once you enter the data you can use the statistical functions to calculate the following 7 Maa and standard deviation m Linear regression statistics m Linear estimation and forecasting Weighted mean Summation statistics 7 Lx Ux Ly Ly and Lary 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 CL The display is 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 QCLY 2 Enter the first value and press The HP 10BII displays 7 the number of items accumulated 3 Continue accumulating values by entering the numbers and pressing The value is incremented with each entry Two
19. 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 are 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 m 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 7 500 00 PMT Money received by lessor is positive 35 36 I YR 10 N 36 Money paid out by lessor is negative P YR 12 PV 13 500 00 Begin Mode Set
20. bis the y intercept Linear Regression Calculate 7 b and r the correlation coefficient as follows 1 Clear the statistical registers by pressing Q CLY 2 Enter the first x value and press 0 The x value is displayed 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 value is incremented with each entry 5 To display the y intercept press Own Then press 9609 to display m the slope of the line 6 Press Neen 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 y value m To estimate x for the given y enter the y value then press QoG To estimate y for the given x enter the x value then press QGq Example Forecasting Ali s Azaleas advertises on a local 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 Minutes of Advertising Sales x values y values 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 ge ee Me
21. by the number of periods in a yeat m 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 2 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 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 JAAG lt 4 Picturing Financial Problems 49 You can calculate any value after entering the other four Cash flow di
22. continuously At the end of each month you deposit 250 00 in the account What will the balance be after 15 years Keys Display Description 0 18 Divides nominal rate by 100 Ce 1 20 Raises e to 0 18 power coooa 19 72 Calculates annual effective rate E 19 72 Stores effective rate DOr 12 00 Sets payments per year Ca von 18 14 Calculates annual nominal rate for a monthly payment period Set to End Mode Press QJ 29 if BEGIN annunciator is displayed DOE 180 00 Stores number of months DOOM 250 00 Stores regular payment DOALA 4 572 80 Stores current balance as a negative value like an initial investment 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 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 t
23. electrical and electronic equipment The separate a collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment For more information about where you can drop off your waste equipment for recycling please contact your local city office your household waste disposal service or the shop where you purchased the product End 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 the period specified above due to defects in material and workmanship when properly installed and used If HP receives notice of such defects 126 A Assistance Batteries and Service during the warranty period HP will replace software media which does not execute its programming instructions due to such defects HP does not warrant that the operation of HP products will be
24. 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 l Initial cash flow 77 28 INT 26 Interest compound 48 simple 47 Interest conversion at a glance 17 Interest 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 51 K L 37 Lease 63 with advance payments 65 Linear regression 19 90 42 Loans 55 98 interest only 102 number 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 Mu 35 N n 88 N 49 N 26 n 42 Natural logarithm 42 Negative numbers 24 Net future value 115 M 78 72 Nominal interest 17 Index 141 NPV 51 ata glance 18 automatic storage of 84 calculating 80 Numbers display format 29 full precision 31 negative 24 range of 131 rounding 32 storing 37 O O
25. mortgage from the lender s point of view 47 510 22 er 82 83 84 a 82 510 22 When you group the above cash flows yow ll find that CF 47 510 22 82 510 22 35 000 CF 861 59 754 00 107 59 N 82 CF 861 59 Ny 180 82 98 Keys Display COMME CFO 35 000 00 RD EDOM HHACH CF1 107 59 gamy n1 82 00 CF2 861 59 MABOOOOQN n2 98 00 ao 10 16 114 8 Additional Examples 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 side 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 years into a money market fund earning 8 8 What is the current balance of the account 12 3 45 6 7 8 910 1 12 13 14 15 16 17 18 19 20 21 22 23 24 3 000 2 000 I YR 8 8 12 000 Current Date Set to End mode Press Qo 29 if BEGIN annunciator is displayed Keys Display Description Ca A Clears all registers oam 12 00 Sets payments per year DOOWOrtRC CFO Enters initial cash flow 12 000 00 OC CF1 Enters amount in 0 00 group 1 DN n1 Enters number of 2 00 times payment occurs DOOOMWCG CF2 Enters amo
26. 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 000P PMT 0 I YR 7 2 N P YR 1 1 2 3 PV 2 000 00 FV 3 000 00 Since this account has no regular payments PMT 0 the payment mode End or Begin is irrelevant Keys Display SED 0 00 DFR 1 00 DAMAHE 2 000 00 DOOMED 3 000 00 DODI 7 20 N 5 83 60 5 Time Value of Money Calculations Description Clears all registers Sets P YR to 1 since interest is compounded annually Stores amount paid out for first deposit Stores the amount you wish to accumulate Stores annual interest rate Calculates number of years it takes to reach 3 000 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 east 3 000 Calculate the actual balance at the end of six years OW 6 00 Sets N to 6 years 3 035 28 Calculates amount you can withdraw after 6 yeats 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 14 201
27. 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 will no longer cycle through interest principal and balance To resume amortization with the same set of periods press RCL ors 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 Qo 9 if BEGIN annunciator is displayed 68 5 Time Value of Money Calculations Keys Display Description DAER 12 00 Sets payments per year Coma 360 00 Stores total number of payments DOOR 7 75 Stores interest per year DOOOOOrRY 180 000 00 Stores present value OE 0 00 Stores future value PMT 1 289 54 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 12_ Enters starting and ending periods a 1 12 Displays the PER annunciator and range 1 579 82 Displays the PRIN annunciator and the principal paid in the first year 13 894 66 Displays the INT annunciator and the interest paid in the first year 178 420 18
28. rate 112 8 Additional Examples Cash Flow Examples Wrap Around Mortgages A 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 are 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 Qo 29 if BEGIN annunciator is displayed Keys Display Description Cay 0 00 Clears all registers TeAm 12 00 Sets payments per year OBOOODOOWOEFY 82 510 22 Stores loan amount on which your new payment is calculated QMOHwr 9 50 Stores interest rate 0 00 Stores final balance TOT 180 00 Stores number of monthly payments you will make PMT 861 59 Calculates your new payment 8 Additional Examples 113 Then to calculate the lender s return enter cash flows that represent the complete picture of the wrap around
29. s compounding periods per year WE 5 13 Calculates annual effective rate CAm 12 00 Stores monthly periods Cap won 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 QJ 29 if annunciator is not displayed 0 00 Stores present value 25 00 Stores payment Maer 84 00 Stores total number of payments 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 are of 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 No A UN N Organize your cash flows on paper A cash flow diagram is useful Clear the registers Enter the number of periods per year Enter the amount of the initial investment Enter the amount of the next cash flow If the amount entered in step 5 occurs more than once consecutively enter the number of times it occurs Repeat steps 5 and 6 for each cash flow and group To calculate net present
30. that two values have been returned Press Q GwaA to see the hidden value Keys Description 6m to Display Cas i Arithmetic mean Mean average of the average of the x values y values if you entered y data Kw Mean of the x values weighted by the y values ES Sample standard Sample standard P P deviation of the x deviation of the y values values if you entered y data 7 Statistical Calculations 87 Keys Description ea to Display Gs Population standard Population standard deviation of the x deviation of the y values values if you entered _y data p value eG Estimate of x fora given Correlation coefficient t value of x value Gon Estimate of y for a given Slope 7 of calculated value of x line omi intercept d of the Slope 7 of the calculated line calculated line The sample standard deviation assumes that the data is a sampling o a larger complete set of data The population 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 positive correlation and 1 indicates a perfect negative correlation A value close to zero indicates the line is a poor fit Keys Description CO Ow CY Cex CF Cby Number of data points entered
31. 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 QJ 9 if annunciator is not displayed 5 Time Value of Money Calculations 65 Keys Display Description AWER 12 00 Sets payments per year DON 47 00 Stores number of payments AQADOOts lun 2 400 00 Stores monthly payment OE 0 00 Stores FV for step 1 OQR 9 00 Stores interest rate 95 477 55 Calculates present value of 47 monthly payments Step 2 Add the additional advance payment to PV Store the answer EMENDO 97 877 55 Adds additional advance payment 97 877 55 Stores result in M register Step 3 Find the present value of the buy option DON 48 00 Stores month when buy option occurs OFM 0 00 Stores zero payment for this step of solution CAMOTE 15 000 00 Stores value to discount 10 479 21 Calculates present value of last cash flow Step 4 Add the results of steps 2 and 3 Keys Display Description ORME 108 356 77 Calculates present capitalized value of lease Rounding discrepancies are explained on page 59 66 5 Time Value of Money Calculations Amortization Amortization is the process of dividing a payment into the amount that applies 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 PAYMENT
32. the current estimate for JRR YR You can resume the calculation by m Pressing QGTO Ge while the current estimate is displayed in the calculator line This continues the calculation from where it left off m Storing a guess for RR YR discussed below Entering a Guess for IRR YR To enter a guess key in an estimate of JRR YR and then press STO wn You can enter a guess for RR YR at these times Before beginning the calculation A fairly accurate guess can reduce the time required to calculate an answer and reduce the chance of the calculator solving for an undesirable negative solution m 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 be found When calculating RR 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 JRR 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 X to Correct Data The HP 10BII stores the statistical numbers
33. value enter the annual interest rate and press WR then press APY Or to calculate annual internal rate of return press f 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 return 6 Cash Flow Calculations 75 11 765 29 Flows received are positive 2 000 00 Flows paid out are negative 4 000 00 5 000 00 Keys Display Description Cary 0 00 Clears all registers OB 12 00 Stores periods per year HOOMOMCH 5 000 00 Enters initial cash flow Displays cash flow group number while you hold down CF DMO 2 000 00 Enters next cash flow DOMO 4 000 00 Enters next cash flow DOMOOOOOCH 11 765 29 Enters final cash flow a 38 98 Calculates annual nominal yield 0G 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 val
34. 0 I YR 6 3 N 360 15 years x 24 half months P YR 24 Half months periods 1 2 3 4 n PMT 80 00 PV 2 000 00 Set to End mode Press e9 if BEGIN annunciator is displayed 5 Time Value of Money Calculations 61 Keys Display Description DOWER 24 00 Sets number of periods per year AOOOtHM E 2 000 00 Stores initial deposit COHEN 80 00 Stores regular semimonthly deposits OOBwr 6 30 Stores interest rate TomT 360 00 Stores number of deposits 52 975 60 Calculates balance Example An Annuity 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 repetitive uniform withdrawal of funds will you receive at the 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 I YR 7 N 600 50 x 12 P YR 12 PV 400 000 00 Begin Mode Set to Begin mode Press wE if annunciator is not displayed 62 5 Time Value of Money Calculations Keys Display Description Qe cia 12 00 Sets payments per year DOOOOOtIFY 400 000 00 Stores your nest egg as an outgoing deposit AYR 7 00 Stores annual interest rate you expect to earn Gom T 600 00 Stores number of withdrawals OE 0 00 Stores balance of account after 50 years PMT 2 392 80 Calculates amount that you can withdraw
35. 0 Enters price MAR 31 82 Calculates margin If the cost is 20 00 and the markup is 33 what is the selling price 2 0 st 20 00 Enters cost 33 00 Enters markup PRC 26 60 Calculates price 12 Ata Glance 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 QQ 200 Display Description 7 00 Stores X 7 as a constant operation 119 00 Multiplies 17 X 7 154 00 Multiplies 22 x 7 175 00 Multiplies 25 x 7 Store 519 in register 2 then recall it SOOT 2 519 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 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 Present value Payment Future value Begin or End mode Number of payments per year mode 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 Qo 9 if BEGIN annunciator is displayed Keys Display Descri
36. 09 are the sample standard deviations They 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 G65 and EI eE 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 GLE DOOM MSB2 mr BE DDAC CACM ax Cam war Ces ETT Cw Display 0 00 1 00 184 25 82 75 5 80 331 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 y Calculates population standard deviation for heights x Displays population standard deviation for weights y Displays the total of the y s Linear Regression and Estimation Linear regression is a statistical method for estimation and forecasting It is used to find a straight line that best fits a set of x y data There must be at least two different x y pairs The straight line provides a relationship between the x and y variables y mx b where m is the slope and
37. 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 Description TACTA 87 50 Calculates loan interest 1 337 50 Adds 87 50 and 1 250 00 to show repayment amount Percent Change L J Calculate the percent change between two numbers 74 and n expressed as a percent of 744 by entering 7 Mo then press Ga Example Calculate the percent change between 291 7 and OS JO 316 8 Keys Display Description oHm 291 70 Enters 74 CTACTA 8 60 Calculates percent change Example Calculate the percent change between 12 x 5 and 65 18 Keys Display Description 60 00 Calculates and enters 74 COTTA 38 33 Calculates percent change 34 2 Business Percentages Margin and Markup Calculations The HP 10BII can calculate cost selling price margin or markup Application Keys Description Margin CST ERO Margin is markup expressed as a percent of price Markup CSD ERO Markup calculations are expressed as a percent of cost To see any value used by the Margin and Markup application press and then the key you wish to see For example to see the value stored as CST press RCD CST Margin and Markup share the same storage register For example if you store 20 in MA then press RCD MU you will see 20 00 displayed Margin Calculations Example Kilowatt Electronics pur
38. 3 000 00 Forecasted e ca 2 000 00 7 m 425 88 Sales in Dollars Y ae x 1 000 00 b Minutes of Advertising 7 Statistical Calculations 91 Keys C OMDOOOM mur DAO Bory DOOM Swen QAOOOEs CMPC Dory DDOE omm om coom 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 J Displays slope Calculates correlation coefficient Estimate what the level of sales would be if the business purchased 7 or 8 minutes of advertising Dei omm 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 COTO k 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 X2 4 Xy occurring with weights y1 yo 1 Use and 2 to enter x y pairs The y values are the weights of the x values 2 Press v 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 CL 0 00 5 0 0 mun 5 4 E 1 00
39. 4 15 16 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 are placed on the horizontal 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 outis negative cash flowing in is positive For example from the lendet 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 m 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 th
40. 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 54 BEGIN 26 55 Begin mode 55 Borrowing equity 113 Buy out value 63 C 25 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 Correlation coefficient 19 88 140 Index Cost 12 Cost of no discount 97 35 Cursor 25 D Decimal places 30 Digit separator 31 Discount 97 Discounted mortgage 99 Discounting cash flows 77 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
41. AO m 20 00 Enters period to amortize Cap ver 20 20 Displays period to amortize 7 25 Displays principal O 115 61 Displays interest Money paid out is negative 13 865 83 Displays balance Amortize the 1 through 12 loan payments 12_ Enters range of periods to amortize Cap vor 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 To convert between nominal and effective interest rates then solve for the unknown rate a T Nominal interest percent wE Effective interest percent SER Periods per year Find the annual effective interest rate of 10 nominal interest compounded monthly Keys Display Description oom 10 00 Enters nominal rate TomT 12 00 Enters payments per year Com FF 10 47 Calculates annual effective interest At a Glance enter the known rate and the number of periods per year 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 60799 Number of consecutive times cash flow J occurs 9 Internal rate of return per year am PY Net present value If you have an initial cash outflow of 40 000 followed by monthly cash inflows of 4 700 7 000 7 000 and 23 000 what is th
42. Calculations 79 To replace a cash flow amount press a COCOA to Qto store the new amount in cash flows 0 to 9 a 6C to to store the new amount in cash flows 10 to 14 n to store the amount in the next cash flow GOCO to store the amount in the previous cash flow n 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 QW Since cash flows cannot be deleted or inserted use QCA 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 QCAY and store the number of periods per year in P YR 2 Enter the cash flows using and N 3 Store the annual nominal interest rate in YR and press PY Example A Discounted Contract Uneven Cash flows You have an opportunity to purchase a contract with the following cash flows End of Month Amount 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 I YR 15 10 000 5 000 5 000 4 910 15 25 Keys Display Description Se 0 00 Clears registers ea Giz 12 00 Sets payments per y
43. 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 equals 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 ine 13 24 Displays PER and the next range of periods G 1 706 69 Displays PRIN and the principal paid in the second year G 13 767 79 Displays INT and the interest paid in the sec ond year 176 713 49 Displays BAL and the loan balance after 24 payments 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 54th 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 we if annunciator is not displayed Keys Display Description DO ary 12 00 Sets payments per yeat omm
44. JRR 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 There might also be additional negative answers m Case 3 The calculator displays a negative answer and no message This is the only answer m Case 4 The calculator displays the message Not Found This indicates that the calculation is very complex It might involve more than one 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 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 C key The message Interrupted is displayed Pressing now displays
45. Sum of the x values Sum of the y values Sum of the squares of the x values Sum of the squares of the y values Sum of the products of the x and y values Mean Standard Deviations and Summation Statistics 88 7 Statistical Calculations You can calculate the mean x sample standard deviation S and population standard deviation O and summation statistics 7 Lx and Xx 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 Xay 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 y x n Keys Display Description am CLE 0 00 Clears statistical registers DOG 1 00 Enters first time DEH 2 00 Enters second time Oey 3 00 Enters third time OOOO 4 00 Enters fourth time BOO 5 00 Enters fifth time Hooe 6 00 Enters sixth time x 3 50 Calculates the mean ES 0 85 Calculates the sample standard deviation Cee 77 13 Displays Xx Gaw 6 00 Displays 7 Gma 3 59 Calculates the root mean square The standard deviations calculated by Q amp S and QQ amp sy 96
46. Terms and conditions 126 Thousands separator 31 Time Value of Money See TVM Troubleshooting 121 Turn off 23 Turn on 23 TVM 53 at a glance 14 15 equations 132 problems 49 TVM 26 Two variable statistics 86 U Uneven cash flow 80 WwW Warranty 122 Weighted mean 86 93 Wrap around mortgages 113 X 42 Y 43 Yield 83 y intercept 88 Index 143
47. 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 twelfth power or 4 0 with the decimal point moved 12 places to the left You can enter this number by pressing DOMO 30 1 Getting Started Displaying the Full Precision of Numbers To set your calculator to display numbers as precisely as possible press QOS G 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 0I8P and hold The number is displayed as long as you continue holding The decimal point is not shown Start with two decimal places Q GSP 2 Keys Display Description MOOME 1 43 Divides E 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 C For example one million can be displayed as 1 000 000 00 or 1 000 000 00 1 Getting Started 31 Rounding Numbers J cents monthly payment Keys Display POGDOGOSe 9 87654321_ SaS 9 88 SaD 987654321000 9 88 0E 988000000000 Messages The calculator stores and calculates using 12 digit numbers When 12 digit accuracy is not desirable use RMD to r
48. agrams 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 I YR 7 5 N 360 30 x 12 357 358 359 360 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 FV 25 327 38 I YR 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 QWPY Net Present Value or Ge Internal Rate of Return per Year 16 567 20 5 000 00 13 14 15 16 12 9 10 N 5 000 00 6 000 00 7 000 00 Cash flow problems are described in chapter 6 4 P
49. al 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 IYR 7 5 N 30 x12 P YR 12 7 Gol lb alg PMT 930 00 End Mode Set to End mode Press Qo 9 if BEGIN annunciator is displayed Keys Display Description lea 12 00 Sets periods per yeat DOLE 360 00 Stores the length of the mortgage 30 X 12 OV 0 00 Pays mortgage off in 30 years MOOR 7 50 Stores interest rate OOdO CEeuD 930 00 Stores desired pay ment money paid out is negative 133 006 39 Calculates the loan you can afford with a 930 payment OOOOOOS 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 Ste
50. ally 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 14 500 1 500 I YR 10 5 N 3x12 P YR 12 PMT End Mode Set to End mode Press Qo 9 if BEGIN annunciator is displayed 5 Time Value of Money Calculations 55 Keys eel iz SYJON a OCON DLEO OOOOrY OE Zx PMT Display 12 00 36 00 10 50 13 000 00 0 00 422 53 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 money paid out Part 2 Ata price of 14 500 what interest rate is necessary to lower your payment by 50 00 to 372 53 HOE I YR 372 53 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 cat to lower your car payment to 375 00 DOON OHOOOOS 56 5 Time Value of Money Calculations 10 50 375 00 11 537 59 13 037 59 Stores origin
51. an annual nominal interest rate and you wish to solve for the corresponding annual effective rate 1 Enter the nominal rate and press wo 2 Enter the number of compounding periods and press fYR 3 Calculate the effective rate by pressing QE To calculate a nominal rate from a known effective rate 1 Enter the effective rate and press EF 2 Enter the number of compounding periods and press ER 3 Calculate the nominal rate by pressing 0 In the TVM application Qo and share the same register Interest conversions are used primarily for two types of problems Comparing investments with different compounding periods m Solving TVM problems where the payment period and the interest period differ 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 yeat 72 5 Time Value of Money Calculations First Bank Keys OOMQ ww DPR om Second Bank OOOG Gator OBR Ce Third Bank OOOB ty CCOR om Display 6 70 4 00 6 87 6 65 12 00 6 63 360 00 6 85 Description Stores nominal rate Stores quarterly compounding periods Calculates annual effective rate Stores nominal
52. arned 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 QJ 29 if BEGIN annunciator is not displayed Keys Display Description OSPR 1 00 Sets 1 payment per year OON 35 00 Stores number of payment periods until retirement BOOMHO 5 89 Calculates interest rate DAWA diminished by tax rate TYR 5 89 Stores adjusted interest rate OFV 0 00 Stores amount you are starting with BDOOM s up 3 000 00 Stores amount of annual payment 345 505 61 Calculates amount in account at retirement O CuDeY 87 556 47 Calculates present value purchasing power of FV assuming a 4 inflation
53. ch 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 1 2 of 1 000 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 1 2 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 1 025 26 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 m Asa periodic rate This is the rate that is applied to your money from period to period m As an annual nominal rate This is the periodic rate multiplied
54. chases televisions for 255 The televisions are sold for 300 What is the margin Keys Display Description 255 00 Stores cost in CST DOWER 300 00 Stores selling price in PRC MAR 15 00 Calculates margin Markup 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 M eEsp 19 00 Stores cost OM 60 00 Stores markup PRC 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 OCOC 9 60 Stores invoice cost 15 00 Stores markup PRC 11 04 Calculates the price on a case of soup MAR 13 04 Calculates margin 36 2 Business Percentages Number Storage and Arithmetic Using Stored Numbers in Calculations You can store numbers for reuse in several different ways m Use Constant to store a number and its operator for repetitive operations m Use 3 Key Memory Cu RM and Ma to store recall and sum numbers with a single keystroke a Use Q6T0 and to store to and recall from the 10 numbered registers Using Constants Use K to store a number and arithmetic operato
55. 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 Batteries and Service 123 If local service is unavailable you can ship the calculator to an authorized HP service center for repait All shipping retmportation 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 m Include your return address and description of the problem m Include proof of purchase date if the warranty has not expired m Include a purchase order check or credit card number plus expiration date VISA or MasterCard to cover the standard repair charge Note that credit cards may not be accepted in
56. dd 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 49 Population standard deviation 88 Powers 43 35 Precision 31 Pv 49 142 Index Present value 49 Price 12 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 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 87 STAT 26 27 Statistics at a glance 19 clearing 19 25 85 entering data 86 estimate 19 estimation 90 forecasting 90 key 27 linear 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 wad 28 T
57. ding a Percent Adding or Subtracting a Percent Percent Change Margin and Markup Calculations Margin Calculations Markup on Cost Calculations Using Margin and Markup Together Number Storage and Arithmetic Using Stored Numbers in Calculations Using Constants Using the M Register Using Numbered Registers Doing Arithmetic Inside Registers Doing Arithmetic Power Operator Using Parentheses in Calculations Picturing Financial Problems How to approach a Financial Problem Signs of Cash Flows Periods and Cash Flows Simple and Compound Interest Simple Interest Compound Interest Interest Rates Two Types of Financial Problems Recognizing a TVM Problem Recognizing a Cash Flow Problem 53 53 54 55 55 60 63 67 72 72 73 75 75 77 77 78 79 80 83 84 85 85 86 86 86 87 87 87 87 88 90 93 Time Value of Money Calculations Using the TVM Application Clearing TVM Begin and End Modes Loan Calculations Savings Calculations Lease Calculations Amortization Interest Rate Conversions Investments With Different Compounding Periods Compounding and Payment Periods Differ Cash Flow Calculations How to Use the Cash Flow Application NPV and IRR YR Discontinuing Cash Flows Organizing Cash Flows Entering Cash Flows Viewing and Replacing Cash Flows Calculating Net Present Value Calculating Internal Rate of Return Automatic Storage of IRR YR and NPV Statistical Calculations Clearing Statistical Data Ent
58. display Or Example Calculate woe then calculate 20 47 2 1 17 Keys Display Description Omg 0 25 Calculates the reciprocal of 4 Boma 4 47 Calculates V20 Sooo 51 67 Calculates V20 47 20 MOMS 1 21 Calculates 1 17 52 88 Completes the calculation Example Calculate natural logarithm e2 Then calculate 790 4 Keys Display Description 00Sa 12 18 Calculates e5 N 2 50 Calculates natural loga rithm of the result MOOHMQ 24 00 Calculates 4 factorial 814 00 Completes calculation 42 3 Number Storage and Arithmetic Power Operator The power operator QW raises the preceding number a y value to the power of the following number x value Example Calculate 125 then find the cube root of 125 Keys Display Description CZCS 1 953 125 00 Calculates 1253 TAOTE 5 00 Calculates the cube Sune 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 30 y 85 12 If you enter DOO 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 Cl
59. e number of times the cash flow is repeated is shown The error annunciator 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 A 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 G 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 3 also shown as 3 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 see page 88 To turn the STATS annunciator off press again For example press followed by amp to recall the sum of the
60. e HP 10BHI all cash flows must occur at either the beginning or end of a period m If more 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 financial 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 compound 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 ea
61. e IRR YR What is the IRR per month Keys Display Description EA 0 00 Clears all memory ole Gz 12 00 Sets payments per year AOOOWOtMCH 40 000 00 Enters initial outflow DDO 4 700 00 Enters first cash flow MOOWC 7 000 00 Enters second cash flow DN 2 00 Enters number of consec utive times cash flow occurs DOMMO 23 000 00 Enters third cash flow n CT 15 96 Calculates IRR YR 0G 1 33 Calculates IRR per month What is the NPV if the discount rate is 10 POM 10 00 Enters I YR SAY 622 85 Calculates NPV 18 Ata Glance Statistics At a Glance number number E number number2 number number C n XY Caw ES E m C a ETT y value k NA x value ag Er Ommy Clear statistical registers Enter one variable statistical data Delete one variable statistical data Enter two variable statistical data Delete two variable statistical data Means of x and y Mean of x weighted by y Sample standard deviations of x and j Population standard deviations of x and y Estimate of x and correlation coefficient Estimate of y y 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 7 and Lxy x data y data 50 90 160 Ata Glance 19 Keys CLE DMGE DIDM CDO xi mT
62. e 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 P How will that affect my payment To answer this question once you have calculated a payment based on one interest rate all you need 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 Qo 9 if BEGIN annunciator is displayed Keys Display Description OS ary 12 00 Sets payments per year DOOOOMrRY 735 000 00 Stores known values DOOD 11 20 CO 360 00 OV 0 00 PMT 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 be and adjust the payment period accordingly 26 compounding periods per year What would be the new term of the loan 3 555 00 Enters new payment AOR 26 00 Sets payments per year for every two weeks N 514 82 Calculates number of b
63. ear OC 0 00 Enters initial cash flow of zero The cash flow number is displayed as long as you hold down the CF key OC 0 00 Enters first cash flow omy 3 00 Enters number of occurrences SMTA 5 000 00 Enters second cash flow OC 0 00 Enters third cash flow DN 4 00 Enters number of occurrences OOOOC 5 000 00 Enters fourth cash flow DN 2 00 Enters number of occurrences OC 0 00 Enters fifth cash flow D 4 00 Enters number of occurrences DATOE 7 500 00 Enters sixth cash flow OC 0 00 Enters seventh cash flow 6 Cash Flow Calculations 81 Keys Display Description Ommy 9 00 Enters number of occurrences DOTT 10 000 00 Enters next cash flow The cash flows that describe your prospective investment are now in the calculator You can press RC CF followed by and RCL Gel 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 15 00 Stores annual interest rate ee NPV 27 199 92 Calculates net present value of stored cash flows See 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
64. ear Sales 1 10 000 2 11 210 3 13 060 4 16 075 5 20 590 Keys Display Description CL 0 00 Clears statistics registers Orn DOOOWE 1 00 Enters first year and sales for that year Doa 2 00 Enters second year s data Ben DOOOWE 3 00 Continues data entry AryvyDOOMOE 4 00 OryQAoOOOOe 5 00 omm 22 000 50 Estimates sales for year six D r 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 If payment is not made within 10 days the full amount must be paid by the 30 day You can use 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 COS TORS eee eee DISC K360 KIO a ee 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 until 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 QWOOWOWDOWB 72 000 00 Calculates numerator in equation SOQROOOMOMQ0 98 00 Parentheses force order
65. ering Statistical Data One Variable Statistics Two Variable Statistics and Weighted Mean Correcting Statistical Data Correcting One Variable Data Correcting Two Variable Data Summary of Statistical Calculations Mean Standard Deviations and Summation Statistics Linear Regression and Estimation Weighted Mean Contents 7 8 117 117 118 119 119 119 119 121 122 122 122 123 Contents Additional Examples Business Applications Setting a Sales Price Forecasting Based on History Cost of Not Taking a Cash Discount Loans and Mortgages Simple Annual Interest Continuous Compounding Yield of a Discounted or Premium Mortgage Annual Percentage Rate for a Loan With Fees Loan With a Partial Odd First Period Automobile Loan Canadian Mortgages What if TVM Calculations Savings Saving for College Costs Gains That Go Untaxed Until Withdrawal Value of a Taxable Retirement Account Cash Flow Examples Wrap Around Mortgages Net Future Value Assistance Batteries and Service Answers to Common Questions Environmental Limits Power and Batteries Low Power Annunciator Battery Specifications Installing Batteries Determining if the Calculator Requires Service Limited One Year Warranty What Is Covered What Is Not Covered Consumer Transactions in the United Kingdom 123 123 124 124 124 125 125 126 129 129 129 130 130 131 131 132 132 132 132 133 134 135 137 139 If the Calculator Requires Service
66. ge register called the M register In most cases it is unnecessary to clear the M register since replaces the previous contents However you can clear the M register by pressing 0 GW To add a series of numbers to the M register use to store the first number and to add subsequent numbers To subtract the displayed number from the number in the M register press followed by M Keys Description 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 DON ADoOos QOOOo OOOGmW Display 17 00 14 25 16 95 4 65 43 55 Description Stores 17 in M register Adds 14 25 to M register Adds 16 95 to M register Adds 4 65 to M register Recalls contents of the M register 3 Number Storage and Arithmetic 39 Using Numbered Registers The Q 610 and keys access the 10 user registers The 9610 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 GGT or RCD To cancel this step press or 2 Enter the register number 0 through 9 In the following example two storage registers are used Calculate the following 475 6 aie 560 1 475 6 39 15 39 15 Ke
67. h up to 99 cash flows per group Ten numbered storage registers m Easy access to functions saves keystrokes and adds convenience e Auto increment capability for amortization schedules e Labels for amortization and cash flows e Automatic constant e 3 key memory Many examples are included in the manual so you can combine them for your specific needs 4 Welcome to the HP 10BIl Contents 11 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 Ata Glance 16 Amortization 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 Messages Contents 5 33 33 34 34 35 35 35 36 37 37 39 40 41 42 43 43 45 46 47 47 47 48 49 49 49 51 6 Contents Business Percentages Percent Key Fin
68. he mortgage is 79 000 Step 1 Calculate PMT Make sure FV 0 Set to End Mode Press QJ e9 if BEGIN annunciator is displayed Keys Display Description Dam 12 00 Sets payments per year UYR 9 00 Stores interest rate DOWEN 240 00 Stores number of months DOOOOMtSCY 100 000 00 Stores original amount of mortgage OEV 0 00 Enters amount left to pay after 20 years PMT 899 73 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 Description RD MT 899 73 Rounds payment to two decimal places for accuracy Om 60 00 Stores number of payments until balloon 88 706 74 Calculates balloon payment add to final payment 100 8 Additional Examples 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 RYNOHAN 18 00 Stores remaining number of payments MOOOOM 79 000 00 Stores price of mortgage YR 20 72 Calculates the return on this discounted mortgage Annual Percentage 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 i
69. hp 10BIl financial calculator user s guide ra Edition 1 HP part number F1902 90001 Notice REGISTER YOUR PRODUCT AT www register hp com 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 NON INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE HEWLETT PACKARD CO 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 EXAMPLES CONTAINED HEREIN Copyright 1988 1989 2001 2004 Hewlett Packard Development Company L P Reproduction adaptation or translation of this manual is prohibited without prior written permission of Hewlett Packard Company except as allowed under the copyright laws Hewlett Packard Company 4995 Murphy Canyon Rd Suite 301 San Diego CA 92123 Printing History Edition 1 May 2003 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 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
70. icturing Financial Problems 51 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 m The amount of each payment must be the same If the payment amounts vary use the procedures described in chapter 6 Cash Flow Calculations m Payments must occur at regular intervals a The payment period must coincide with the interest compounding period If it does not convert the interest rate using the a amp i WE and GYR 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 The number of payments or compounding periods YR 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 PMI 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 EYR Stores the n
71. in an accumulated fashion It doesn t store every number that you enter but rather it performs intermediate calculations when you press the key The QJ key performs the opposite intermediate calculations to effectively remove a number or pait of numbers from the stored results When correcting statistical data does not delete rounding errors that may occur during the intermediate calculations done by Thus subsequent results for corrected data may be different than for data that was entered originally without having to use JG 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 are 1 x 104 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 COS MAR T x 100 Mu COST x 100 Time Value of Money TVM Payment Mode Factor S 0 for End mode 1 for Begin mode jj ZR P YR i 1 zy 100 1 100 0 Pv 14 2X5 0 x PMT x o7 N FVx 1 2 100 Amortization XINT accumulated
72. interest XPRN accumulated principal 7 periodic interest rate BAL is initially PV rounded to the current display setting PMT is initially PMT rounded to the current display setting ___I YR P YRx 100 132 B More About Calculations For each payment amortized INT INT PRN BAL new XINT new XPRN new BAL X i INT is rounded to the current display setting INT 0 for period 0 in Begin mode INT with sign of PMT PMT INT BAL 1g PRN SINT 4 INT DPRN y PRN Interest Rate Conversions P YR EFF 1 Au 1 x100 100 x P YR B More About Calculations 133 Cash Flow Calculations 1 Nj NPV When NPV return periodic interest rate the group number of the cash flow amount of the cash flow for group number of times the cash flow occurs for group the group number of the last group of cash flows yn total number of cash flows prior to group l lt l lt j i jie 1 zy CF CFx N E xX pe hl gt J h m 100 0 the solution for 7 is the periodic internal rate of 134 B More About Calculations Statistics n n yy 2 yx Sx 2 n 1 2 yy 22 eae 2 2 TE ryt a or s oy aeaa n n E yxy he po ee ee e AS bee pS b m oe y mx b B More About Calculations 135 Messages Press or to clear a message from the display All Clear Memory has been erased page 25 COPR HP 2000
73. iweekly payments C79 19 80 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 Display Description DOr 12 00 Sets payments per year DOQQ 180 00 Stores new term PMT 8 446 53 Calculates payment for shorter term WRVOA 1 520 374 70 Calculates total paid EVG 785 374 70 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 are 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 month 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 I YR 9
74. kard against defects in materials and workmanship for one year from the date of original purchase If 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 ptepaid 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 states provinces or countries do not allow limitations on how long an implied warranty lasts so the ab
75. l Examples Description Sets payments per yeat 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 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 payme
76. nes page 26 Ata Glance 21 Getting Started Power On and Off L JIE eT OOOO J To turn on your HP 10BH press N To turn the calculator off press the orange shift key then N also written Q Since the calculator has continuous memory turning it off does not affect the information you have stored To conserve energy the calculator turns itself 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 ot Simple Arithmetic Calculations Arithmetic Operators The following examples demonstrate using the arithmetic operators and If you press more than one operator consecutively for example 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 87 18 Adds 24 71 and 62 47 balaas Ai When a calculation has been completed by pressing pressing a number key starts a new calculation DOWDOAOOWOW 240 92 Calculates 19 X 12 68 If you press an operator key after completing a calculation the calculation is continued OHOOOOOS 356 42 Completes calculation of 240 92 115 5
77. nt 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 Qo 29 if BEGIN annunciator is displayed Keys Display Description DAER 12 00 Sets payments per year ONR 15 00 Stores interest rate ooga 1 25 Calculates periodic interest rate DOOWOOW 0 67 Multiplies by fraction of a period DEMME 30 00 Calculates amount of simple interest owed for odd period PACOY 4 530 00 Adds this simple interest to present value 8 Additional Examples 103 BOW Or PMT Automobile Loan 36 00 0 00 157 03 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 m 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 Qo 9 if BEGIN annunciator is displayed Calculate the first option Keys DSE OW DAMAY QOGONR Qe 9 amp 2 T a ae 104 8 Additional Examples Display 12 00 36 00 12 500 00 0 00 3 50 366 28 13 185 94 Description Sets payments per yeat Stores known values Stores first interest rate
78. nterest 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 QJ 29 if BEGIN annunciator is displayed Keys Display Description eleie ci 12 00 Sets payments per year OCORA 8 50 Stores interest rate OOH 360 00 Stores length of mortgage DOOWOOWR 160 000 00 Stores original amount of mortgage 8 Additional Examples 101 OW 0 00 PMT 1 230 26 160 000 00 TAAT 156 800 I YR 8 72 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 znterest only loan has an origination fee of three points What is the yield to the lender Assume that monthly payments of interest are made Set to End mode Press Qo 9 if BEGIN annunciator is displayed Keys Display oam Ti 12 00 ANR 12 00 DO 120 00 DOWOMOWOMFY 1 000 000 00 ED 1 000 000 00 PMT 10 000 00 1 000 000 00 SAE 970 000 00 YR 12 53 102 8 Additiona
79. of calculation ACCOA 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 DEMY 0 10 Stores interest KAOTA 7 40 Calculates interest owed ORMG 457 40 Calculates total owed Continuous Compounding The equation for calculating an effective rate for continuous compounding is NOM 100 EFF e 1 x100 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 this 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 8 Additional Examples Example You currently have 4 572 80 in an account at Dream World Investments that earns 18 annual interest compounded
80. osing 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 DOGSOOHO 85 00 No calculation yet OOO 73 00 Calculates 85 12 0 41 Calculates 30 73 Oe 3 70 Multiplies the result by 9 44 3 Number Storage and Arithmetic Picturing Financial 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 ot remaining amount to designate a value that the HP 10BII knows as 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 12 13 1
81. ound the number to the displayed format before using it in a calculation Rounding numbers is useful when you want the actual dollars and Description Enters a number with more than two non zero decimal places Displays two decimal places Displays all digits with out the decimal while you press Rounds to two decimal places specified by pressing Q GSA D Shows rounded stored number The HP 10BI 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 or See 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 UU J ia adding or subtracting a percent J The key has two functions finding a percent and 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 DOO 200 00 Enters 200 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 Description BDOOO 200 00 Enters 200 50 00 Multiplies 200 by 0 25 150 00 Subtracts 50 from
82. ount 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 are 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 Q 29 if BEGIN annunciator is not displayed Keys Orr DON SOOLON OY DOEN RD EMAED WE HRD WOOWS CHORD EWS OoAOCMDEY 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 rate Stores amount you start with Stores amount of annual payment Calculates amount in account at retirement Calculates amount you have paid into account by retirement Calculates interest account has e
83. ove 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 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 for the location of the nearest service center Do not ship the calculator for service without first
84. owing steps 1 Press GCA to clear the resisters 2 Enter the number of periods per year and press fR 3 Enter the amount of the initial investment then press CF The 4 stands for the cash flow number 0 through 14 4 Enter the amount of the next cash flow and press CF 5 If the amount entered in step 4 occurs more than once consecutively enter the number of times it occurs and press QW 6 Repeat steps 4 and 5 for each and QW 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 eA 0 00 Clears all registers DASR 12 00 Sets YA to 12 ODOOOOMG 11 000 00 Enters initial cash flow Displays cash flow group number for as long as you hold down CFi 0 CF 0 00 Enters first cash flow group amount Cw 6 00 Enters number of repetitions POMOC 1 000 00 Enters second cash flow group amount omy 3 00 Enters number of repetitions TOTTI 10 000 00 Enters final cash flow OER 21 22 Calculates annual nominal yield Viewing and Replacing Cash Flows To view a cash flow press m ROCO to to display cash flows 0 to 9 or a ROCO to Mto display cash flows 10 to 14 m to display the next cash flow m ROCO to display the previous cash flow m to display the current cash flow 6 Cash Flow
85. p 1 First calculate the loan payment using a 25 year term PV 172 500 I YR 8 8 N 25 x12 P YR 12 299 300 PMT End Mode Set to End mode Press Qo 9 if BEGIN annunciator is displayed Keys Display Description oam Ti 12 00 Sets periods per year oom 300 00 Stores length of mortgage 25 X 12 300 months O 0 00 Stores loan balance after 25 years OMAOOWrY 172 500 00 Stores original loan balance OOGUN 8 80 Stores annual interest rate PMT 1 424 06 Calculates monthly 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 I YR 8 8 N 4x12 P YR 12 44 45 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 OSP 2 Display Description RND 1 424 06 Rounds payment to two decimal places then stores DON 48 00 Stores 4 year term 12 x 4 that you expect to own house 163 388 39 Calculates loan bal ance after 4 years me 164 812 45 Calculates total 48 payment PMT and FV to pay off loan money paid out is negative 5 Time Value
86. ption CASER 12 00 Sets payments per year DOOW 360 00 Enters number of payments DOR 10 00 Enters interest per year ONOOOWErY 14 000 00 Enters present value Ov 0 00 Enters future value PMT 122 86 Calculates payment if paid at end of period 14 Ata Glance TVM What if At a Glance 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 CESS L ae Keys Display Description MOM lun 100 00 Enters new payment amount Money paid out is negative 11 395 08 Calculates amount you can borrow How much can you borrow at a 9 5 interest rate OCO 9 50 Enters new interest rate 11 892 67 Calculates new present value for 100 00 payment and 9 5 interest DONR 10 00 Reenters original interest rate OMHOOOrRY 14 000 00 Reenters original present value PMT 122 86 Calculates original payment Ata Glance 15 Amortization At a Glance After calculating a payment using Time Value of Money TVM enter the periods to amortize and press Q or Then press to continually cycle through the principal interest and balance values indicated by the PRIN INT and BAL annunciators respectively Using the previous TVM example page 14 amortize a single payment and then a range of payments Amortize the 20 payment of the loan Keys Display Description
87. r 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 Operation B number OE OC number OE Od number K number K Ax value K Q Q D Daumber h number h number number h OOO k Stores number as constant Stores number as constant Stores X number as constant Stores number as constant Stores y ale as constant Stores number as constant Stores number as constant Stores X number as constant Stores number as constant Example Calculate 5 2 64 Keys Sow MS 2 and 7 2 Display Description 2 00 Stores 2 as constant 7 00 Adds 5 2 8 00 Adds 6 2 9 00 Adds 7 2 Example Calculate 10 10 11 10 and 25 10 Keys MOCWOCMK 200 Example Calculate 2 and 4 Keys QAQvOwW Display Description 1 00 Stores 10 as constant 11 00 Adds 10 to 10 12 10 Adds 10 to 11 27 50 Adds 10 to 25 Display Description nau Stores y3 as con stant 8 00 Calculates 2 38 3 Number Storage and Arithmetic e 64 00 Using the M Register Calculates 4 The M RM and keys perform memory operations on a single stora
88. rate Stores monthly com pounding periods Calculates annual effective rate Stores nominal rate Stores compounding periods 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 payment period complete the following steps 1 Enter the nominal rate and press Qo Enter the number of compounding periods in a year and press YR Solve for the effective rate by pressing QuEF 2 Enter the number of payment periods in a year and press fR Solve for the adjusted nominal rate by pressing Qawow 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 Gm 5 00 Stores nominal percentage rate oomai 365 00 Stores bank
89. th two decimal places and a period as the decimal point The display format controls how many digits appear in the display J 80005 If the result of a calculation is a number containing 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 QJGSP 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 QoisA 0 000 Displays three decimal places DOLOK 5 727 OOOOO m 5 727360000 Displays nine decimal places SOSA 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 X 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 1414
90. to Begin mode Press QJ 29 if annunciator is not displayed Keys Display Description CASER 12 00 Sets payments per year DOR 10 00 Stores desired annual yield OHOOOOtMEY 13 500 00 Stores lease price DOMME 7 500 00 Stores residual buy out value GON 36 00 Stores length of lease in months EMD 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 market 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 for a 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 9 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
91. tor 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 ON 4 If the calculator is still not responding erase the memory see below and repeat steps 1 to 3 above one more time Erasing the calculator s memory 1 Hold down the N key 2 Hold down the N and then the 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 see 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 department The address and phone number are listed on the inside back cover Limited One Year Warranty What Is Covered The calculator except for the batteries or damage caused by the batteries is warranted by Hewlett Pac
92. ts m Operating temperature 0 to 40 C 32 to 104 F m 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 __ 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 battery cover Accessing the battery compartment A Assistance Batteries and Service 119
93. ue NPV function finds the 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 znitial 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 the 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 one 10 000 cash flow 6 Cash Flow Calculations 77 CF 3 10 000 N3 1 CF 2 1 000 N 2 3 CF1 0 N1 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 foll
94. umber of periods per year The default is 12 Reset only when you wish to change it This key is located below the key SEN 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 N key a Switches between Begin and End mode In Begin mode the BEGIN annunciator is displayed a vor Calculates an amortization table To verify values press RCD N RCD YA RCD Pv RCL EMD and Rc EV Pressing RCD Qe recalls the total number of payments in years and RCL ewf shows you the number of payments per year Recalling these numbers does not change the content of the registers Clearing TVM Press C 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 5 Time Value of Money Calculations Begin and End Modes Before you start a TVM calculation identify whether the first periodic payment occurs at the beginning or end of the first period If the first payment occurs at the end of the first period set your HP 10BII to End mode if it occurs at the beginning of the first period set your calculator to Begin mode To switch between modes press Qo 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 typic
95. 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 entitled to a refund of the purchase price upon prompt return of the product HP products may contain remanufactured parts equivalent to new in performance or may have been subject to incidental use Warranty does not apply to defects resulting from a improper or inadequate maintenance or calibration b software interfacing parts or supplies not supplied by HP c unauthorized modification ot misuse d operation outside of the published environmental specifications for the product or e improper site preparation or maintenance 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 might not 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 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 e
96. unt in 3 000 00 en omy n2 Enters number of 3 00 times payment occurs ooon n3 Enters number of 3 00 times payment occurs MOOOtMC CF4 Enters cash flow group 7 500 00 4 OCD Le Enters number of times payment occurs 8 Additional Examples 115 DOA COET APY ON OPMT 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 Pm not sure if the calculator is malfunctioning or if Pm 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 numbers contain commas instead of periods as decimal points How do I restore the periods A Press Qo page 31
97. vent 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 ot 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 For consumer transactions in Australia and New Zealand the warranty terms contained in this statement except to the extent lawfully permitted do not exclude restrict or modify and are in addition to the mandatory statutory rights applicable to the sale of this product to you A Assistance Batteries and Service 127 More About Calculations IRR YR Calculations The calculator determines RR 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 one solution to the calculation However calculating IRR YR for certain sets of cash flows is more complex There may be more than one or no mathematical solution to the 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
98. x values entered 1 Getting Started 27 INPUT Key It Ji The key is used to separate two numbers when using COOCOO two number functions or two variable statistics The key can also be used to evaluate any pending arithmetic operations in which case the result is the same as pressing SWAP Key ij Pressing 6 exchanges the following m 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 a The x and y values when using statistics Math Functions One Number Functions Math functions involving one number use the number in the display 80000 loss Qoo Keys Display Description CLAC 9 45 Calculates square root CQCOAOG 0 42 1 2 36 is calculated first OUCH 3 99 Adds 3 57 and 1 2 36 28 1 Getting Started Two Number Functions When a function requires two J i 00000 numbers the numbers are entered like this nwmberl ee number2 followed by the operation Pressing evaluates the current expression and displays the INPUT annunciator For example the following keystrokes calculate the percent change between 17 and 29 Keys Display Description 17 00 Enters number displays the INPUT annunciator D 29_ Enters number2 70 59 Calculates the percent change Display Format of Numbers J When you turn on the HP 10BII for the first time numbers are displayed wi
99. ys Display Description MMOO0OE9 475 60 Stores 475 60 dis played number in Ry COOVMHASs9 2 39 15 Stores 39 15 in Ro 12 15 Completes first calculation CCMA 475 60 Recalls R4 SRD 39 15 Recalls Rp 26 45 Completes second calculation With the exception of statistics you can also use 610 and RCD for application registers For example GTO WR stores the number from 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 previous contents However you can clear a single register by storing 0 in it To clear all the registers at once press D 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 Keys New Number in Register ET A register number Old contents displayed number E O register number Old contents displayed number ET X register number Old contents X displayed number ET O register number Old contents displayed number Example Store 45 7 in Ra multiply by 2 5 and store the result in R4 Keys Display Description DOODS 45 70 Stores 45 7 in R3 DOOS 2 50 Multiplies 45 7 in R3 by 2 5 and stores result 114 25 in R3 114 25 Displays R3 3 Number Storage and Arithmetic 41 Doing Arithmetic Math functions operate on the number in the

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