Question

If a $1,200 investment earns $210 over 5 years, what is the annual interest rate?

Answer 1

Answer:

The annual interest rate is 41.7%.

Step-by-step explanation:

Given : If a $1,200 investment earns $210 over 5 years.

To find : What is the annual interest rate?

Solution :

Using compound interest formula,

$A=P(1+r)^t$

Where, A=$1200 is the amount

P=$210 is the principal

t=5 years is the time

r is the interest rate.

Substitute the value,

$1200=210(1+r)^5$

$\frac{1200}{210}=(1+r)^5$

$5.714=(1+r)^5$

Taking 5th root both side,

$\sqrt[5]{5.714}=(1+r)$

$1.417=(1+r)$

$r=1.417-1$

$r=0.417$

Interest rate in percentage, $r=0.417\times 100=41.7\%$

The annual interest rate is 41.7%.