Question

Mr. Bert deposited $5,000 into an investment account with an annual interest rate of 3.75%. How much will his investment be worth in 15 years?(1 point) Responses $593,622.67 $593,622.67 $77,812.50 $77,812.50 $8,685.44 $8,685.44 $5,050.26

Answer 1

To calculate the future value of Mr. Bert's investment, 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 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:
- \(P = 5000\)
- \(r = 0.0375\) (3.75% as a decimal)
- \(n = 15\)

Plugging in the values:

\[
A = 5000(1 + 0.0375)^{15}
\]
\[
A = 5000(1.0375)^{15}
\]

Calculating \( (1.0375)^{15} \):

\[
(1.0375)^{15} \approx 1.7493
\]

Now calculating the future value \(A\):

\[
A \approx 5000 \times 1.7493 \approx 8746.50
\]

Based on this calculation, the investment would be worth approximately **$8,746.50** after 15 years.

Thus, among the provided response options, the closest amount is **$8,685.44**, which may account for rounding differences.

So, the final answer is **$8,685.44**.