Question

Mr. Bert deposited $5,000 into an investment account with an annual interest rate of 3.75%. How much will his investment account be worth in 15 years?

answer choices:
A
$593,622.67

B
$77,812.50

C
$8,685.44

D
$5,050.26

Answer 1

To calculate the future value of Mr. Bert's investment account, we'll use the formula for compound interest:

\[ A = P(1 + r/n)^{nt} \]

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 times that interest is compounded per year.
- \( t \) is the time the money is invested for in years.

In this case:
- \( P = 5000 \)
- \( r = 0.0375 \)
- \( n = 1 \) (assuming interest is compounded annually)
- \( t = 15 \)

Plugging the values into the formula:

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

Now, calculating \( (1.0375)^{15} \):

\[ (1.0375)^{15} \approx 1.747422 \]

Now, multiply this by the principal amount:

\[ A \approx 5000 \times 1.747422 \]
\[ A \approx 8737.11 \]

So, Mr. Bert's investment account will be worth approximately **$8,737.11** after 15 years. This value doesn't match any answer choices exactly, but it's closest to:

C) $8,685.44

Therefore, the answer is **C** $8,685.44.