Question

If you invest $4000 at 9% interest compounded annually, in how many years will you have $20,000. Give your answer the nearest tenth of year?

Answer 1

18.7 years

Explanation:

This is a compound interest problem and the following variables have been given;

Principal = 4000; this is the amount o be invested

APR = 9%; this is the compound interest to be earned

Accumulated amount = 20,000

We are required to determine the duration in years. We apply the compound interest formula;

`A=P(1+r)^(n)`

`20000=4000(1+(9)/(100))^(n)\\20000=4000(1.09)^(n)\\5=(1.09)^(n)`

The next step is to introduce natural logarithms in order to determine n;

`ln5=nln(1.09)\\n=(ln5)/(ln(1.09))\\n= 18.675`

The number of years required is thus 18.7 years