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

Answer:

18.7 years

Step-by-step 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;

$A=P(1+r)^{n}$

$20000=4000(1+\frac{9}{100})^{n}\\20000=4000(1.09)^{n}\\5=(1.09)^{n}$

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

$ln5=nln(1.09)\\n=\frac{ln5}{ln(1.09)}\\n= 18.675$

The number of years required is thus 18.7 years