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]
