Question
Tom takes out a loan of $20,000 with a 7% annual compounded interest rate. If he pays it back in three years, what will be his total repayment amount?
Answers
GPT-4o mini
To calculate the total repayment amount for a loan with compound interest, you can use the formula for compound interest:
\[
A = P(1 + r)^n
\]
where:
- \( A \) is the total amount to be repaid,
- \( P \) is the principal amount (the initial loan),
- \( r \) is the annual interest rate (in decimal),
- \( n \) is the number of years the money is borrowed.
Given:
- \( P = 20,000 \) (the loan amount),
- \( r = 0.07 \) (7% annual interest rate),
- \( n = 3 \) (the loan period in years).
Now, substituting the values into the formula:
\[
A = 20000(1 + 0.07)^3
\]
Calculating \( (1 + 0.07)^3 \) first:
\[
1 + 0.07 = 1.07
\]
\[
(1.07)^3 = 1.07 \times 1.07 \times 1.07 \approx 1.225043
\]
Next, multiply this by the principal:
\[
A \approx 20000 \times 1.225043 \approx 24500.86
\]
Therefore, Tom's total repayment amount after three years will be approximately **$24,500.86**.
\[
A = P(1 + r)^n
\]
where:
- \( A \) is the total amount to be repaid,
- \( P \) is the principal amount (the initial loan),
- \( r \) is the annual interest rate (in decimal),
- \( n \) is the number of years the money is borrowed.
Given:
- \( P = 20,000 \) (the loan amount),
- \( r = 0.07 \) (7% annual interest rate),
- \( n = 3 \) (the loan period in years).
Now, substituting the values into the formula:
\[
A = 20000(1 + 0.07)^3
\]
Calculating \( (1 + 0.07)^3 \) first:
\[
1 + 0.07 = 1.07
\]
\[
(1.07)^3 = 1.07 \times 1.07 \times 1.07 \approx 1.225043
\]
Next, multiply this by the principal:
\[
A \approx 20000 \times 1.225043 \approx 24500.86
\]
Therefore, Tom's total repayment amount after three years will be approximately **$24,500.86**.