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.
1 answer