Question

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

Answer 1

The annual interest rate is 41.7%.

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`

`(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* 100=41.7\%`

The annual interest rate is 41.7%.