Robin, who is self-employed, contributes $5,500/year into a Keogh account. How much will he have in the account after 15 years if the account earns interest at the rate of 8.5%/year compounded yearly?

Answer 1

Suppose the amount after n years is A(n), and he deposits $ 5500 at time zero.

Then A(0) = 5500 and we need A(15)

To find A(n+1) multiply A(n) by 1.085 (adds 8.5% interest per year) and add 5500

So A(0) = 5500

A(n+1) = 1.085 A(n) + 5500

A(1) = 1.085 X 5500 + 5500 = 11467.50

A(2) = 11467.50 x 1.085 + 5500 = 17942.24

etc.

In theory you can work forward to A(15) however you are likely to get some small rounding errors coming in.

The general result is a(n) = (p^n) a(0) + r (1- p^n) / (1 - p)

a(0) = 5500, n = 15, p = 1.085, r = 5500