Question

Derek deposited $7,000 in an account earning 15% interest compounded annually.
To the nearest cent, how much interest will he earn in 3 years?

Answer 1

To calculate the amount of interest earned on an account with compound interest, we can use the formula:

\[
A = P(1 + r)^n
\]

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial deposit).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.

Given:
- \( P = 7000 \)
- \( r = 0.15 \) (15% as a decimal)
- \( n = 3 \)

Let's first calculate the total accumulation after 3 years.

\[
A = 7000(1 + 0.15)^3
\]

Calculating \( (1 + 0.15)^3 \):

\[
(1 + 0.15) = 1.15
\]
\[
1.15^3 \approx 1.15 \times 1.15 \times 1.15 \approx 1.520875
\]

Now we can calculate \( A \):

\[
A \approx 7000 \times 1.520875 \approx 10646.125
\]

Now, to find the interest earned, we subtract the principal from the total amount:

\[
\text{Interest} = A - P = 10646.125 - 7000 \approx 3646.125
\]

To the nearest cent, the interest Derek will earn in 3 years is:

\[
\text{Interest} \approx 3646.13
\]

So, Derek will earn **$3646.13** in interest in 3 years.