Chaper 10.6

An installment loan is a series of equal payments made at equal time intervals for the purpose of paying off a lump sum of money received up front. These are things like the loan for the purchase of a car or the mortgage on a home. The most important difference between an installment loan and a deferred annuity is that an installment loan has a present value that we calculate by adding the present value of each payment, whereas a deferred annuity has a future value that we compute by adding the future value of each payment.

Example 1: Financing that Mustang Convertible

Let’s suppose that you have just landed a really good job and have decided to by that cherry red Mustang convertible. You negotiate a really good price of $23,995 (including taxes and fees). You have $5,000 as a down payment and you can get a car loan from the dealership for 60 months at 6.48% annual interest compounded monthly. If you take out the loan from the dealer for the balance of $18,995, what would your monthly payments be? Can you afford them? *Most people blindly accept whatever the finance department at the dealership tells them that they can afford. This is why there are all those shows on reality TV about Repo men!!

Every time that you make a future payment on an installment loan, that payment has a present value. The sum of all of those present values is equal to the present value of the loan that you have taken out, in this case, $18,995. Although each monthly loan payment of F has a different present value, each of these present values can be calculated using the general compounding formula: The present value P of a payment of $F paid T months in the future is

where p = the periodic pr monthly interest rate.

P = Present value of the future payment

F = the value of the future payment

T = nt. the number of times interest is compounded times the number of years

p = r/n

r = annual percentage rate

n = number of times compounded per year

In our example, the values are as...