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To solve this problem, we use the compound interest formula:

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

Where:
- $A$ is the amount after interest,
- $P$ is the principal (initial deposit) = \$12,000,
- $r$ is the annual interest rate (decimal form) = 3% = 0.03,
- $n$ is the number of times the interest is compounded per year (monthly compounding means $n = 12$),
- $t$ is the number of years = 9.

Substitute the values into the formula:

\[
A = 12000 \left( 1 + \frac{0.03}{12} \right)^{12 \times 9}
\]

Now, let's calculate it step by step.

1. First calculate the monthly interest rate:
\[
\frac{0.03}{12} = 0.0025
\]

2. Add 1 to the monthly rate:
\[
1 + 0.0025 = 1.0025
\]

3. Multiply the number of times the interest is compounded by the number of years:
\[
12 \times 9 = 108
\]

4. Now raise $1.0025$ to the power of 108:
\[
1.0025^{108} \approx 1.28203723171
\]

5. Multiply this result by the principal:
\[
12000 \times 1.28203723171 \approx 15484.45
\]

Thus, the amount after 9 years will be approximately **\$15,484.45**.

Would you like any further details on the calculation or the steps?

---

1. What is the difference between simple and compound interest?
2. How does increasing the number of compounding periods (monthly vs. yearly) affect the total interest earned?
3. What happens if the interest rate increases or decreases?
4. Can you explain the concept of annual percentage yield (APY)?
5. How would the calculation change if the deposit was made for 10 years instead of 9?

**Tip:** When dealing with compound interest, even small increases in the interest rate or the number of compounding periods can have a significant effect on the final amount.

Use the formula for computing future value using compound interest to determine the value of an account at the end of 9 years if a principal amount of $12,000 is deposited in an account at an annual interest rate of 3% and the interest is compounded monthly.

Learn how to calculate the future value of $12,000 at 3% annual interest compounded monthly over 9 years. The step-by-step solution uses the compound interest formula A = P(1 + r/n)^(nt), perfect for high school students in Grades 9-12.

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