1. Finance Models M 110 Modeling with Elementary Functions V.J. Motto

2. Finance Application We will use the FINANCE programs for compound interest Press APPS button Then ENTER (or 1) to choose the option FINANCE

3. Guide to the Variables. N – the term of the account I% – Annual interest rate (entered as a percent, not a decimal) PV – Deposit (or Present Value, a negative number) FV – Balance of the account after N years (or Future Value) P/Y – Number of payments per year C/Y – Number of compoundings per year PMT – END

4. Some Comments There are two default values that must be set for all compound interest problems Set PMT = 0 because there are no payments. Set P/Y = 1 since there is 1 payment per year. PV is entered as a negative value because it is an “out flow of cash.” The last line (PMT) should be set to END since your account is compounded at the end of each time period.

5. Example 1 An investor has $5,000 to invest in a long-term certificate of deposit (CD) paying 7.5% interest compounded annually. a. What will the account be worth in three years. b. When will the CD be worth $10,000 Here we have the following N = 3 I% = 7.5 PV = - 5000 PMT = 0 FV = ? P/Y = 1 C/Y = 1 PMT : END

6. Solution to 1 a You should fill in the variables as show to the left. When you are done, place the cursor next to the FV (Future Value) variable. Then press SOLVE; that is, ALPHA + ENTER. What did you get for the result? ($6,211.48)

7. Solution to 1 b This problem is a little different. You are asking when the CD will be worth $10,000? You know the Future Value but not N, the number of years. So set up your calculator as show to the right. Then press SOLVE; that is, ALPHA + ENTER. What did you get for the result? (9.6 years)

8. Example 2 A young couple wants to have $20,000 in five years for a down payment on a house. An annual interest rate of 8% compounded quarterly is available. How much must they invest now? Here we know the following: N = 5 I% = 8 PV = ? PMT = 0 FV = 20000 P/Y = 1 C/Y = 4 PMT : END

9. Solution to 2 So they would need to invest $13,459.42 You can set your calculator to automatically round to 2 decimal places!