Question

Kim put $8,000.00 in a savings account that offers 6% interest compounded annually. Kim makes no additional deposits or withdrawals. Which amount is closest to the interest she will have earned at the end of 10 years?

Answer 1

To calculate the interest earned on an investment compounded annually, we can use the formula for compound interest:

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

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

In Kim's case:
- \( P = 8000 \)
- \( r = 0.06 \) (6%)
- \( n = 10 \)

Now plug in these values into the formula:

\[
A = 8000(1 + 0.06)^{10}
\]
\[
A = 8000(1.06)^{10}
\]

First, calculate \( (1.06)^{10} \):

\[
(1.06)^{10} \approx 1.790847
\]

Now multiply this by the principal:

\[
A \approx 8000 \times 1.790847 \approx 14326.776
\]

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

\[
\text{Interest} = A - P = 14326.776 - 8000 \approx 6326.776
\]

Therefore, Kim will have earned approximately **$6,326.78** in interest at the end of 10 years.