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?
A
$593,622.67
B
$77,812.50
C
$8,685.44
D
$5,050.26
Answers
GPT-4o mini
To calculate the future value of Mr. Bert's investment account, we can use the formula for compound interest:
\[
A = P(1 + r)^t
\]
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).
- \( t \) is the number of years the money is invested or borrowed.
In this case:
- \( P = 5,000 \)
- \( r = 3.75/100 = 0.0375 \)
- \( t = 15 \)
Now we can calculate:
\[
A = 5000 \times (1 + 0.0375)^{15}
\]
Calculating inside the parentheses first:
\[
1 + 0.0375 = 1.0375
\]
Now raising \( 1.0375 \) to the power of 15:
\[
1.0375^{15} \approx 1.7137
\]
Now multiply by the principal:
\[
A \approx 5000 \times 1.7137 \approx 8568.50
\]
The correct value for Mr. Bert's investment account after 15 years is approximately $8,568.50.
This value is closest to option C: $8,685.44.
So the answer is **C: $8,685.44**.
\[
A = P(1 + r)^t
\]
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).
- \( t \) is the number of years the money is invested or borrowed.
In this case:
- \( P = 5,000 \)
- \( r = 3.75/100 = 0.0375 \)
- \( t = 15 \)
Now we can calculate:
\[
A = 5000 \times (1 + 0.0375)^{15}
\]
Calculating inside the parentheses first:
\[
1 + 0.0375 = 1.0375
\]
Now raising \( 1.0375 \) to the power of 15:
\[
1.0375^{15} \approx 1.7137
\]
Now multiply by the principal:
\[
A \approx 5000 \times 1.7137 \approx 8568.50
\]
The correct value for Mr. Bert's investment account after 15 years is approximately $8,568.50.
This value is closest to option C: $8,685.44.
So the answer is **C: $8,685.44**.