Question
Calculate the amount to be paid back on a $20,000 loan with an interest rate of 12% compounded yearly after five years.(1 point)
Responses
$35,246.83
$35,246.83
$51,470
$51,470
$640,000
$640,000
$1,030,726
Responses
$35,246.83
$35,246.83
$51,470
$51,470
$640,000
$640,000
$1,030,726
Answers
GPT-4o mini
To calculate the amount to be paid back on a $20,000 loan with an interest rate of 12% compounded yearly after five years, you 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 loan amount).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is borrowed for.
In this case:
- \( P = 20,000 \)
- \( r = 0.12 \) (12% expressed as a decimal)
- \( n = 5 \)
Now, plug these values into the formula:
\[
A = 20,000(1 + 0.12)^5
\]
Calculate \( (1 + 0.12)^5 \):
\[
(1 + 0.12)^5 = (1.12)^5 \approx 1.762341
\]
Now, multiply this by the principal:
\[
A \approx 20,000 \times 1.762341 \approx 35,246.83
\]
Thus, the amount to be paid back after five years is approximately **$35,246.83**.
The correct response is:
**$35,246.83**
\[
A = P(1 + r)^n
\]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial loan amount).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is borrowed for.
In this case:
- \( P = 20,000 \)
- \( r = 0.12 \) (12% expressed as a decimal)
- \( n = 5 \)
Now, plug these values into the formula:
\[
A = 20,000(1 + 0.12)^5
\]
Calculate \( (1 + 0.12)^5 \):
\[
(1 + 0.12)^5 = (1.12)^5 \approx 1.762341
\]
Now, multiply this by the principal:
\[
A \approx 20,000 \times 1.762341 \approx 35,246.83
\]
Thus, the amount to be paid back after five years is approximately **$35,246.83**.
The correct response is:
**$35,246.83**