Question

Vijay inherited some money from his grandfather and put it in a bank account that earns 6% interest compounded annually. After 3 years, Vijay had $4,000.00 in the bank account. How much interest did he earn? Round your answer to the nearest cent.

Answer 1

We have in this question a case of Annual Compound Interest. The formula for this case is as follows:

`A=P(1+r)^n_{}_{}`

Where:

A = accrued amount.

P = Principal (starting amount).

r = interest rate.

n = number of years.

We have from the question:

r = 6%

n = 3 years.

P = $4,000.00

A = it is the unknown amount.

We can determine A to then find the interest he earned. Thus, we can proceed as follows:

`A=4000(1+0.06)^3\Rightarrow A=4000(1.06)^3\Rightarrow A=4764.064`

This previous amount is the accrued amount (the starting amount plus the interest after 3 years annually compounded).

Therefore, the amount Vijay earned in interests (after 3 years) is:

`4764.064-4000=764.064`

And, rounding this amount to the nearest cent, we have that, finally, the earned interest (after 3 years) is $764.06.