Name: Kim
Who is asking: Parent
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?

Thanks for your help.

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

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

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

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

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

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