Answer :
Let's solve the problem step-by-step using the given formula for annual compound interest:
[tex]\[ A = P \left(1 + \frac{r}{n} \right)^{nt} \][/tex]
Where:
- [tex]\( A \)[/tex] is the total amount owed
- [tex]\( P \)[/tex] is the principal amount (\[tex]$9,000) - \( r \) is the annual interest rate (0.08 or 8%) - \( n \) is the number of times the interest is compounded per year (1, since the interest is compounded annually) - \( t \) is the number of years (3 years) Plug in the values: - Principal \( P = 9{,}000 \) dollars - Annual interest rate \( r = 0.08 \) - Number of times interest compounded per year \( n = 1 \) - Number of years \( t = 3 \) Now substitute these values into the formula: \[ A = 9{,}000 \left(1 + \frac{0.08}{1} \right)^{1 \cdot 3} \] This simplifies to: \[ A = 9{,}000 \left(1 + 0.08 \right)^3 \] \[ A = 9{,}000 \left(1.08 \right)^3 \] Next, calculate \( (1.08)^3 \): \[ 1.08^3 \approx 1.259712 \] Now, multiply this result by the principal amount: \[ A = 9{,}000 \times 1.259712 \approx 11{,}337.408 \] So, the total amount that Tom would repay, rounded to the nearest dollar, is \( \$[/tex]11{,}337 \).
Therefore, the correct answer is:
[tex]\[ \boxed{11{,}337} \][/tex]
[tex]\[ A = P \left(1 + \frac{r}{n} \right)^{nt} \][/tex]
Where:
- [tex]\( A \)[/tex] is the total amount owed
- [tex]\( P \)[/tex] is the principal amount (\[tex]$9,000) - \( r \) is the annual interest rate (0.08 or 8%) - \( n \) is the number of times the interest is compounded per year (1, since the interest is compounded annually) - \( t \) is the number of years (3 years) Plug in the values: - Principal \( P = 9{,}000 \) dollars - Annual interest rate \( r = 0.08 \) - Number of times interest compounded per year \( n = 1 \) - Number of years \( t = 3 \) Now substitute these values into the formula: \[ A = 9{,}000 \left(1 + \frac{0.08}{1} \right)^{1 \cdot 3} \] This simplifies to: \[ A = 9{,}000 \left(1 + 0.08 \right)^3 \] \[ A = 9{,}000 \left(1.08 \right)^3 \] Next, calculate \( (1.08)^3 \): \[ 1.08^3 \approx 1.259712 \] Now, multiply this result by the principal amount: \[ A = 9{,}000 \times 1.259712 \approx 11{,}337.408 \] So, the total amount that Tom would repay, rounded to the nearest dollar, is \( \$[/tex]11{,}337 \).
Therefore, the correct answer is:
[tex]\[ \boxed{11{,}337} \][/tex]
