Date: Wed, 30 Jun 1999 16:11:01 -0600 (CST)
Subject: consumer math

Name: Kim
Level: Secondary

In early 1997, my son borrowed \$4831 at 7.5%. He has made 30 monthly payments of \$130 each. He is now in a position to pay off the balance. What is his remaining principal?

Hi Kim,

What your son will get here is a great lesson in the effects of compound interest. It is unpleasant but an important lesson when bying a car or a house.

I am going to assume that you mean that the interest rate is 7.5% per year, compounded monthly. The way to look at the problem is to think of the \$4831 being invested, 30 months ago, at a rate of 7.5% per year compounded monthly, its value will become

 4831(1 + (.075/12)) = \$4861.19 after one month, 4831(1 + (.075/12))2 = \$4891.58 after two months, ... ..., 4831(1 + (.075/12))30 = \$5823.90 after 30 months.

Thus what your son has to repay is the equivalent of this \$5823.90.

Assuming that he made his first payment at the end of the first month, this payment has grown, after the intervening 29 months (using the same intereest rate), to

130(1 + (.075/12)29).

Similarly , his second payment will grow (after the intervening 28 months) to

130(1 + (.075/12)28).

...

Similarly , his 29th payment will grow (after the intervening 1 month) to

130(1 + (.075/12)1),

and his last payment will 'grow' (after the intervening 0 months) to

130.

Thus his payments are equivalent to the sum of

130(1 + (.075/12)29) + 130(1 + (.075/12)28) + ... +130(1 + (.075/12)1) + 130 = \$4274.95.

(You need to understand how to sum geometric series to do this arithmetic.)

Thus your son still owes \$5823.90 - \$4274.95 = \$1548.95.

Quite a lot! Nothing like \$4831 - 30(\$130)!

Cheers,
Penny

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