Question

Debbie has $4,000 in an account. The interest rate is 15% compounded annually. To the nearest cent, how much interest will she earn in 2 years? $

Answer 1

To calculate the interest earned on an account with compound interest, you 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 amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.

In this case:
- \( P = 4000 \)
- \( r = 15\% = 0.15 \)
- \( n = 2 \)

Let's calculate \( A \):

\[
A = 4000(1 + 0.15)^2
\]
\[
A = 4000(1.15)^2
\]
\[
A = 4000(1.3225)
\]
\[
A = 5290
\]

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

\[
\text{Interest} = A - P
\]
\[
\text{Interest} = 5290 - 4000
\]
\[
\text{Interest} = 1290
\]

Thus, the interest Debbie will earn in 2 years is **$1,290.00**.