Calculator User Guide
Contents
1. Resets the default values 2ND gt P Y gt 12 gt ENTER Enters a monthly payment period V gt 2 gt ENTER Enters a semi annual interest calculation period CE C gt CE C Exits the entry of the C Y variable 75 000 gt gt PV PV 75 000 Enters the loan amount 6 5 gt I Y V Y 6 5 Enters the nominal interest rate 20 gt 2ND gt xP Y gt N N 240 Enters the number of monthly payments over a 20 year period CPT gt PMT PMT 555 3753129 Calculates the amount of the monthly payment Do not clear the values of the financial variables 6 gt I Y Y 6 Enters the second nominal interest rate CPT gt PMT Therefore 555 38 534 14 21 24 PMT 534 1413314 Calculates the amount of the monthly payment 13 Answer 2 ten years rounded off a 6 b 7 c 8 d 9 e 10 The correct answer is b Reason Sequence of entries CE C gt 2ND gt CLR TVM Display AUTORIT _ DES MARCHES FINANCIERS What nominal rate compounded semi annually lets you double your capital in Explanation Resets the default values 2ND gt P Y gt 2 gt ENTER Enters a semi annual payment period CE C gt CE C Exits the entry of the C Y variable 10 gt 2ND gt xP Y gt N Enters the number of monthly payments over a 10 year period 1 000 gt gt PV PV 1 0002. Enters the present value of the investment 2 000 gt FV FV 2 000 Enters the final value of the Investment CPT gt I Y Y 7 052984768 Calculates the semi annual interest rate Note The values of 1 000 and 2 000 were chosen arbitrarily Any value and double that amount would have given the same answer Answer 3 You are thinking about purchasing a 10 000 bond maturing at par in nine years with annual coupons at the rate of 7 How much will you have to pay if you want a compound annual return of 8 a 4 372 82 b 9 002 49 c 9 375 31 d 10 000 00 e 10 375 31 14 The correct answer is C Reason Sequence of entries CE C gt 2ND gt CLR TVM Display 0 AUTORIT DES MARCHES FINANCIERS Explanation Resets the default values 2ND gt P Y gt 1 gt ENTER P Y 1 Enters an annual payment period CE C gt CE C 0 Exits the entry of the C Y variable 10 000 gt FV FV 10 000 Enters the value of the bond at maturity 9 gt N N 9 Enters the number of periods 8 gt I Y Y 8 Enters the annual interest rate CPT gt PV PV 5 002 489671 Calculates the present value of the bond CE C gt 2ND gt CLR TVM 0 Resets the default values 700 gt PMT PMT 700 Enters the value of a coupon 7 x 10 000 8 gt I Y Y 8 Enters the annual interest rate 9 gt N
3. What nominal rate compounded semi annually lets you double your capital in ten years rounded off a 6 7 8 QO O 9 10 D You are thinking about purchasing a 10 000 bond maturing at par in nine years with annual coupons at the rate of 7 How much will you have to pay if you want a compound annual return of 8 a 4 372 82 b 9 002 49 c 9 375 31 d 10 000 00 e 10 375 31 11 Question 4 Question 5 What will your mortgage loan balance be after four years if the following conditions apply round off to the nearest dollar Amount of the loan 110 000 Interest rate 8 2 Term of the loan 25 years with monthly repayments a 103 361 b 93 360 c 83 953 d 98 360 e 100 630 What is the cumulative value after seven years of a monthly investment of 500 made at the end of each month if the nominal rate is 9 12 round off to the nearest dollar a 48 213 b 43 000 c 53 000 d 55 813 e 58 213 12 AUTORIT _ DES MARCHES FINANCIERS Answer Sheet Answer 1 AUTORIT DES MARCHES FINANCIERS You borrow 75 000 to buy a house and agree to repay the loan in 20 years at an interest rate of 6 5 2 How much lower would your monthly payment be with an interest rate of 6 2 a 555 38 b 534 15 c 21 24 d 24 21 e 34 24 The correct answer is C Reason Sequence of entries Display CE C gt 2ND gt CLR TVM Explanation
4. the loan 20 years 240 monthly payments capital borrowed 85 000 The monthly mortgage repayment can be calculated using the following operations Sequence of entries Display Explanation CE C gt 2ND gt CLR Resets the default values TVM 2ND gt P Y gt 12 gt Enters a monthly payment period ENTER V gt 2 gt ENTER Enters a semi annual interest calculation period CE C gt CE C Exits the entry of the C Y variable 20 gt 2ND gt xP Y gt N N 240 Enters the number of monthly payments over a 20 year period 6 gt I Y IY 6 Enters the nominal interest rate 85 000 gt gt PV PV 85 000 Enters the loan amount CPT gt PMT PMT 605 3601756 Calculates the monthly repayment amount To repay this loan over a 20 year period the monthly repayment amount would be 605 36 AUTORIT _ DES MARCHES FINANCIERS The balance of the mortgage loan after five years is calculated using the following operations after having computed the monthly payment of 605 36 Sequence of entries Display Explanation Do not change the data already entered for the financial variables 5 gt 2ND gt xXP Y gt N N 60 Enters the number of monthly payments over a five year period CPT gt FV Calculates the loan balance after 60 monthly payments FV 72 076 74454 The balance of the mortgage loan after five years is therefore 72 076 74 In financial mathematics
5. AUTORIT DES MARCH S FINANCIERS USER GUIDE Texas Instrument BA Il Plus Calculator April 2007 AUTORIT DES MARCH S FINANCIERS GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas of financial analysis and banking AUTORIT _ DES MARCHES FINANCIERS The explanations below will make it easier for you to use the calculator Q By default the calculator operates in financial mode a The ON OFF key is used to turn the calculator on and off Q The 2ND key is often used to access financial applications Press this key when you want to apply the functions displayed in yellow at the top of the keys 1 The FORMAT feature lets you select the number of decimal points to be displayed by the calculator If you want to display gt a fixed decimal point press 2ND and then FORMAT enter a number from 0 to 8 to specify the number of decimal points and then press ENTER gt a floating decimal point press 2ND and then FORMAT enter the number 9 and then press ENTER The number of decimals displayed will vary depending on the calculations up to a maximum of nine decimals To perform the calculator exercises in this document it is best to use a floating decimal point format Q Setting the number of payment periods and interest calculation periods in a financial calculation the P Y and C Y functions gt P Y function this function se
6. BGN 2ND and SET sequence the BGN indicator will disappear The CE C key clears the on screen data without deleting any numerical values that have been entered The CLR TVM function cancels the numeric values and calculation commands and resets the calculator s default financial values Before performing each calculation users are advised to cancel all previously used numerical values by pressing the 2ND and CLR TVM keys These keys however do not affect the beginning of year payment BGN mode or end of period payment END mode or the values attributed to P Y and C Y Therefore it is important to make sure that these values have been programmed before performing a calculation v AUTORIT DES MARCHES FINANCIERS FINANCIAL CALCULATIONS Most financial calculations are carried out using the following seven keys IN Thenumberotperods PMT The periodic payment of an amortized loan or a split annuity Indicates whether the calculations include the payments made at the beginning or at the end of each period Note By convention the present value of an investment is a negative value The calculator is programmed this way therefore in calculations of future values or per period payments if the present value is entered as a negative value the future value or the value of the payments will be positive The opposite is also true It is therefore important to be thorough and refer to the calculator s user guide if ne
7. N 9 Enters the number of periods CPT gt PV PV 4 372 821538 Calculates the present value of interest coupons Therefore the amount payable is 5 002 49 4 372 82 9 375 31 Answer 4 What will your mortgage loan balance be after four years if the following conditions apply round off to the nearest dollar Amount of the loan 110 000 Interest rate 8 2 Term 25 years with monthly repayments a 103 361 b 93 360 c 83 953 d 98 360 e 100 630 15 AUTORIT _ DES MARCHES FINANCIERS The correct answer is a Reason Sequence of entries Display Explanation CE C gt 2ND gt CLR TVM 0 Resets the default values 2ND gt P Y gt 12 gt P Y 12 Enters a monthly payment period ENTER gt 2 gt ENTER C Y 2 Enters a semi annual interest calculation period CE C gt CE C O Exits the entry of the C Y variable 25 gt 2ND gt xP Y gt N N 300 Enters the number of monthly payments over a 25 year period 8 gt I Y IY 8 Enters the nominal interest rate 110 000 gt gt PV PV 110 000 Enters the loan amount CPT gt PMT PMT 839 5348005 Calculates the amount of monthly paymenis After four years Do not clear the values of the financial variables 21 gt 2ND gt xP Y gt N N 252 Enters the number of monthly payments over 21 years CPT gt PV PV 103 360 9468 Calculates the loan balance after 48 monthly payments The mortgage bal
8. ance after four years is 103 361 Answer 5 What is the cumulative value after seven years of a monthly investment of 500 made at the end of each month if the nominal rate is 9 12 round off to the nearest dollar a 48 213 b 43 000 c 53 000 d 55 813 e 58 213 The correct answer is e 16 AUTORIT DES MARCHES FINANCIERS Reason Sequence of entries Display Explanation CE C gt 2ND gt CLR TVM gt 2ND gt CLR TVM a Resets the default values 2ND gt P Y gt 12 gt ENTER Enters a monthly payment period CE C gt CE C Exits the entry of the P Y variable 7 gt 2ND gt xP Y gt n Enters the number of monthly payments over seven years 9 gt 1 Y Y 9 Enters the nominal interest rate 500 gt gt PMT PMT 500 Enters the amount of the monthly investment CPT gt FV FV 58 213 46422 Calculates the cumulative value after seven years The cumulative value after seven years is 58 213 17
9. cessary Sample calculation of the future value FV of a single payment Someone wishes to invest 4 000 in a registered retirement savings plan RRSP for a five year period Insurer A proposes an annual compound interest rate of 6 whereas insurer B proposes a nominal rate of 5 95 compounded on a semi annual basis The following two tables should help you determine which insurer is proposing the best investment AUTORIT _ DES MARCHES FINANCIERS Insurer A Sequence of entries CE C gt 2ND gt CLR TVM Display 0 AUTORIT _ DES MARCHES FINANCIERS Explanation Resets the default values 2ND gt P Y gt 1 gt ENTER PY Enters an annual payment period CE C gt CE C 0 Exits the entry of the P Y variable 5 gt N N 5 Enters a five year period 6 gt Y IY 6 Enters an annual interest rate of 6 4 000 gt gt PV PV 4 000 Enters the present value of the investment CPT gt FV Insurer B Sequence of entries CE C gt 2ND gt CLR TVM FV 5 352 90231 Display Calculates the final value of the Investment Explanation Resets the default values 2ND gt P Y gt 2 gt ENTER Enters a semi annual payment period CE C gt CE C Exits the entry of the P Y variable 5 gt 2ND gt xP Y gt N Enters the number of periods over five years 5 95 gt I Y VY 5 95 Enters a nominal interest rate
10. it is often a good idea to double check calculations In this example another way to calculate the mortgage balance after 5 years would be to calculate the present value of monthly payments of 605 36 over 15 years i e the remaining term of the loan The balance of the mortgage loan after five years can be calculated using the following operations Sequence of entries Display Explanation CE C gt 2ND gt CLR TVM Resets the default values 2ND gt P Y gt 12 gt ENTER Enters a monthly payment period V gt 2 gt ENTER Enters a semi annual interest calculation period CE C gt CE C Exits the entry of the C Y variable 15 gt 2ND gt xP Y gt N Enters the number of monthly payments for the 15 remaining years 6 gt I Y Y 6 Enters the nominal interest rate 605 3601756 gt PMT PMT 605 3601756 Enters the amount of the monthly payments CPT gt PV PV 72 076 74454 Calculates the loan balance after 60 monthly payments The balance of the mortgage loan after five years is therefore 72 076 74 10 AUTORIT _ DES MARCHES FINANCIERS Self Evaluation Exercise Question 1 Question 2 Question 3 You borrow 75 000 to buy a house and agree to repay the loan in 20 years at an interest rate of 6 5 2 How much lower would your monthly payment be with a 6 2 interest rate a 555 38 b 534 15 c 21 24 d 24 21 e 34 24
11. made at the end of the year Sequence of entries CE C gt 2ND gt CLR TVM Display Explanation Resets the default values 2ND gt BGN gt 2nd gt SET Activates the calculation of end of period payments 2ND gt PY gt 1 gt ENTER PY 1 Enters an annual payment period CE C gt CE C 0 Exits the entry of the P Y variable 2 500 gt gt PMT PMT 2 500 Enters the amount of the annual Investment 5 gt N N 5 Enters the number of periods 5 gt I Y VY 5 Enters the annual interest rate CPT gt FV FV 13 814 07812 Calculates the cumulative value of the annuity Obviously an investment made at the beginning of the year will result in a higher cumulative value other variables being equal as the interest will begin to accumulate on the very first day AUTORIT DES MARCHES FINANCIERS Calculating the payment of a personal or mortgage loan The process of calculating a personal or mortgage loan consists of o Determining the known variables 2 Entering the number of payment periods P Y and the number of interest calculation periods C Y Q Calculating the unknown variable Sample calculation of a personal loan repayment Mary wants to borrow 15 000 to purchase a new car and she wants to repay the loan over a five year period If the bank demands a nominal rate of 6 compounded on a monthly basis what would be the monthl
12. of 5 95 4 000 gt gt PV PV 4 000 Enters the present value of the investment CPT gt FV FV 5 362 632027 Calculates the final value of the Investment The investment proposed by Insurer B returns a greater cumulative value after five years of approximately 9 73 Calculating the future value of an annuity A client would like to invest 2 500 per year over the next five years He would like to know what the cumulative value of the investment would be in five years if the annual realized rate were 5 in a situation where the investment is made at the beginning of the year and in a situation where the investment is made at the end of the year AUTORIT DES MARCHES FINANCIERS gt 2 500 investment made at the beginning of the year Sequence of entries CE C gt 2ND gt CLR TVM Display Explanation Resets the default values 2ND gt BGN gt 2ND gt SET Activates the calculation of beginning of period payments 2ND gt PY gt 1 gt ENTER Enters an annual payment period CE C gt CE C 0 Exits the entry of the P Y variable 2 500 gt gt PMT PMT 2 500 Enters the amount of the annual Investment 5 gt N N 5 Enters the number of periods 5 gt I Y VY 5 Enters the annual interest rate CPT gt FV FV 14 504 78203 Calculates the cumulative value of the annuity gt 2 500 investment
13. ts the number of annual payments The default value is one payment per year To change the number of annual payments press the 2ND and P Y keys enter the required value and then press ENTER for example 12 for 12 monthly payments gt C Y function this function sets the number of interest calculation periods By default the number of interest calculation periods is the same as the number entered for the P Y variable To change it press 2ND P Y and and then enter the number of periods and press ENTER Example where the C Y differs from the P Y monthly payments on a personal loan on which interest is calculated quarterly I 4 Sequence of entries Display Explanation 2ND gt P Y gt 12 gt ENTER P Y 12 Enters a monthly payment period 12 months 2ND gt P Y gt V gt 4 gt Enters a quarterly interest ENTER calculation period 4 three month periods per year N B It is important to follow the sequence of entries without pressing any other key Q Q Q The BGN function lets you activate the beginning of period or the end of period payment To understand the configuration of this function simply press the 2ND and BGN keys To the left of your screen you will then see the END or BGN letters To activate the beginning of period payment calculation simply press the 2ND BGN 2ND and SET keys The BGN indicator then appears in the upper right area of the display screen To return to END simply repeat the 2ND
14. y repayment end of period Known variables nominal rate 6 12 term of the loan five years 60 monthly payments capital borrowed 15 000 Number of annual payments 12 Number of interest calculation periods 12 The monthly repayment can be calculated using the following operations Sequence of entries Display Explanation CE C gt 2ND gt CLR TVM Resets the default values 2ND gt P Y gt 12 gt ENTER Enters a monthly payment period CE C gt CE C Exits the entry of the P Y variable Enters the number of monthly payments 5 gt 2ND gt xP Y gt N over five years 6 gt I Y VY 6 Enters the nominal interest rate 15 000 gt gt PV PV 15 000 Enters the amount of the loan Calculates the amount of the monthly CPT gt PMT PMT 289 9920229 payments To repay this loan over a five year period the monthly repayment amount would be 289 99 AUTORIT _ DES MARCHES FINANCIERS Sample calculation of a mortgage loan repayment Claude buys a home for 125 000 and makes a 40 000 cash downpayment To finance the balance the bank offers him an 85 000 mortgage loan at a nominal rate of 6 compounded on a semi annual basis What monthly payments will be required to repay this mortgage over a 20 year term What will the mortgage balance be after five years To answer these two questions the known variables must first be determined nominal rate 6 2 term of
Download Pdf Manuals
Related Search