1 The TVM Solver The TVM Solver is an application on the TI-83 Plus graphing calculator. It displays the timevalue-of-money (TVM) variables used in solving finance problems. Prior to using the TVM Solver, press MODE and set the Float at 2. This will cause decimal answers to display with 2 digits - useful since most answers in finance are in dollars and cents. To access the TVM Solver, press the dark blue APPS key, select 1: Finance, then 1: TVM Solver. A screen appears with the following variables: N = total number of payment periods I% = annual interest rate PV = present value PMT = payment amount FV = future value P/Y = number of payment periods per year C/Y = number of compounding periods per year PMT: indicates whether payments are made at the end or beginning of each payment period When you input four of the first five variables in the list above, the TVM Solver solves for the fifth variable. Enter money invested as a negative number. Cash outflows are considered negative, while cash inflows, including loans, are considered positive. P/Y is the number of payment periods per year in a financial transaction. C/Y is the number of compounding periods per year in the same transaction. When you store a value to P/Y, the value for C/Y automatically changes to the same value. To store a unique value to C/Y, you must store the value to C/Y after you have stored a value to P/Y. To solve, move the cursor to the fifth variable. Press ALPHA, then ENTER to access 'solve' and calculate the value of this variable. A small shaded box to the left of the variable indicates a solution.
2 example 1: What can an investor expect to receive at the end of a year if he deposits $200 in a bank giving 10% per year interest, compounded annually? solution: The first column below shows the values that must be entered for the variables. A zero is placed beside 'FV', the variable to be N = 1.00 N = 1.0 I% = 10.00 I% = 10.00 PV = -200.00 PV = -200.00 FV = 0 FV = 220.00 The investor would receive $220.00. example 2: You invest $800 in an account at 8% per year, compounded semiannually. Determine the accumulated amount of your investment after 5 years. variables. A zero is placed beside 'FV', the variable to be N = 5 x 2 N = 10.00 I% = 8.00 I% = 8.00 PV = -800.00 PV = -800.00 FV = 0.00 FV = 1184.20 P/Y = 2.00 P/Y = 2.00 C/Y = 2.00 C/Y = 2.00 Your accumulated amount after 5 years will be $1184.20
3 example 3: How long will it take a dollar to double invested at 8% per year, compounded semiannually? variables. A zero is placed beside 'N', the variable to be solved for 'N'. N = 0 N = 17.67 I% = 8.00 I% = 8.00 PV = -1.00 PV = -1.00 FV = 2.00 FV = 2.00 P/Y = 2.00 P/Y = 2.00 C/Y = 2.00 C/Y = 2.00 It takes 17.67 payment periods, or 17.67 half-years, which is about 9 years. example 4: What can Mavis withdraw from her account if she saves $1000 a year for 3 years at 5% per year, compounded annually? variables. A zero is placed beside 'FV', the variable to be N = 3.00 N = 3.00 I% = 5.00 I% = 5.00 PV = 0.00 PV = 0.00 PMT = -1000.00 PMT = -1000.00 FV = 0.00 FV = 3152.50 In three years, Mavis can withdraw $3152.50.
4 example 5: What monthly payment would Angela make to pay off a used car loan of $2000 at 12% per annum, compounded monthly, by the end of the year? zero is placed beside 'PMT', the variable to be calculated. Because there are monthly payments for a year, 12 is entered for the 'N', the number of payments. 'PV' is entered as a positive 2000 because Angela has the money "in hand". The second column shows the results after having solved for 'PMT'. N = 12.00 N = 12.00 I% = 12.00 I% = 12.00 PV = 2000.00 PV = 2000.00 PMT = 0.00 PMT = -177.70 FV = 0.00 FV = 0.00 P/Y = 12.00 P/Y = 12.00 The monthly payment will be $177.70 note: The monthly payment (PMT) is negative on the calculator screen because it represents the amount Angela must pay out every month. example 6: You invest $200 in an account at 5.5% per year, compounded annually. Each year you pay $300 into the account. What is the accumulated amount of the investment after 9 years? zero is placed beside 'N', the variable to be calculated. The second column shows the results after having solved for 'N'. N = 9 N = 9 I% = 5.5 I% = 5.5 PV = -200.00 PV = -200.00 PMT = -300.00 PMT = -300.00 FV = 0 FV = 3700.696709 After 9 years, the accumulated amount of the investment is about $ 3700.70.
5 example 7: A car you want to buy costs $9000. You can afford payments of $250 per month for four years. What annual percentage rate will make it possible for you to afford the car? zero is placed beside 'I', the variable to be calculated. The second column shows the results after having solved for 'I'. N = 12.00 X 4 N = 48.00 I% = 0 I% = 14.90 PV = 9000.00 PV = 9000.00 PMT = -250.00 PMT = -250.00 FV = 0.00 FV = 0.00 P/Y = 12.00 P/Y = 12.00 example 8: At what annual interest rate, compounded monthly, will $1250 accumulate to $2000 in 7 years? zero is placed beside 'I', the variable to be calculated. The second column shows the results after having solved for 'I'. N = 7.00 N = 7.00 I% = 0 I% = 6.73 PV = -1250.00 PV = -1250.00 FV = 2000.00 FV = 2000.00 After 9 years, the accumulated amount of the investment is about $ 3700.70