To calculate the amount to be paid back on a loan with compound interest, we can use the formula:
\[ A = P(1 + r)^n \]
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)
- \( n = 5 \)
Substituting the values into the formula:
\[ A = 20,000(1 + 0.12)^5 \]
Calculating the value further:
\[ A = 20,000(1.12)^5 \]
Calculating \( (1.12)^5 \):
\[ (1.12)^5 \approx 1.76234 \]
So,
\[ A \approx 20,000 \times 1.76234 \approx 35,246.83 \]
Thus, the amount to be paid back after five years is approximately $35,246.83.
So, the correct response is:
$35,246.83