Amortization M 110 Modeling with Elementary Functions V.J. Motto

Paying off a loan The technical term for paying off a loan is amortization. When we amortize (bring to death) a loan we are killing a debt, that is, reducing it to zero through a series of periodic (equal) payments. We will be using our TI-calculator to determine these monthly payments.

Guide to the Variables. N – the number of payments – years * number of payments per year I% – Annual interest rate (entered as a percent, not a decimal) PV – Amount you owe (or Present Value, negative number) PMT – Your periodic payment FV – 0 (You wish to reduce your balance to zero) P/Y – Number of payments per year C/Y – Save value as P/Y PMT – END (Payments are due at the end of each period)

Example 1 The Manufacturer’s Suggested Retail Price (MSRP) for a 2003 Mazda Miate is $19,280. An annual interest rate of 3.5% can be negotiated with a credit union if you agree to a five-year loan for the total amount. (The credit union does not require a down payment) a. What will your payment be? b. How much total interest will you pay? c. What would be your answer if you could pay off the loan in 3 years at the same interest rate. Here we have the following N = 60 I% = 3.5 PV = PMT = ? FV = 0 P/Y = 12 C/Y = 12 PMT : END

Solution to 1 So the monthly payment is $ Hence, 60($350.74) -$19280 = $1, in interest. This is 5 payments or 11% of the purchase price. What happens if you change N from 60 to 36? Try it!

Example 2 A high ranking state official accumulate $90,000 in credit card debt. Suppose that he makes no more purchases and that the current annual rate for his credit is 18% What monthly payment must he make to pay the loan off in four years? How much total interest will he pay? How much of his first payment will be applied to his balance? Here we know the following: N = 48 I% =18 PV = PMT = ? FV = 0 P/Y = 12 C/Y = 12 PMT : END

Solution to 2 The total interest paid is 48($2,643.75) - $90,000 = $36,900 roughly 41% of the original debt. Interest charges for the first payment are (.18/12)*$90,000 = $1,350, which means that less than half of his first payment ($1, ) would be applied to the balance.