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 $1,030,726 $1,030,726 $640,000 $640,000 $35,246.83 $35,246.83 $51,470
Answers
GPT-4o mini
To calculate the amount to be paid back on a loan with compound interest, 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).
- \( r \) 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% is expressed as 0.12 in decimal)
- \( n = 5 \)
Now, plug in the values:
\[
A = 20,000(1 + 0.12)^5
\]
Calculate \( (1 + 0.12)^5 \):
\[
1.12^5 \approx 1.76234
\]
Now multiply by the principal:
\[
A \approx 20,000 \times 1.76234 \approx 35,246.83
\]
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).
- \( r \) 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% is expressed as 0.12 in decimal)
- \( n = 5 \)
Now, plug in the values:
\[
A = 20,000(1 + 0.12)^5
\]
Calculate \( (1 + 0.12)^5 \):
\[
1.12^5 \approx 1.76234
\]
Now multiply by the principal:
\[
A \approx 20,000 \times 1.76234 \approx 35,246.83
\]
Thus, the amount to be paid back after five years is approximately **$35,246.83**.
The correct response is: **$35,246.83**.