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This problem involves compound interest, where we need to find the future value of a loan that grows annually at a given interest rate.

The formula for compound interest is:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount owed after $ t $ years.
- $ P $ is the principal amount (initial loan), which is $46,000.
- $ r $ is the annual interest rate, 3.25% or 0.0325.
- $ n $ is the number of times interest is compounded per year. Since it's compounded annually, $ n = 1 $.
- $ t $ is the time the money is invested or borrowed, which is 9 years.

Plugging the values into the formula:

\[
A = 46,000 \left(1 + \frac{0.0325}{1}\right)^{1 \times 9}
\]

\[
A = 46,000 \left(1 + 0.0325\right)^9
\]

\[
A = 46,000 \left(1.0325\right)^9
\]

Now, let's calculate the future value.

\[
A = 46,000 \times (1.0325)^9
\]
\[
A \approx 46,000 \times 1.3276 \approx 61,070.60
\]

Rounding this to the nearest dollar:

\[
A \approx 61,071
\]

Thus, the amount owed after 9 years is **$61,071**.

Would you like a detailed explanation of each step? 

Here are five related questions you might explore:
1. How would the final amount change if the interest were compounded monthly instead of annually?
2. What is the difference in the final amount if the interest rate were 4% instead of 3.25%?
3. How much interest is accrued over the 9 years?
4. How would the future value change if payments were made during the 9 years?
5. What would happen if the loan term were extended to 15 years?

**Tip**: Always make sure to convert percentages into decimal form when using formulas!

An amount of $46,000 is borrowed for 9 years at 3.25% interest, compounded annually. Assuming that no payments are made, find the amount owed after 9 years. Round your answer to the nearest dollar.

Solve the compound interest problem where a $46,000 loan is borrowed for 9 years at 3.25% interest, compounded annually. Learn how to apply the compound interest formula to find the final amount owed after 9 years, rounded to the nearest dollar.

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