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To solve this problem, we’ll use the future value formula for compound interest:

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

where:
- $ P $ is the principal amount (initial investment), which is $10,000.
- $ r $ is the annual interest rate. Here, it’s given as 0.3% per month, so we’ll convert it to an annual rate by multiplying by 12: $ 0.3\% \times 12 = 3.6\% $ per year, or 0.036 in decimal form.
- $ n $ is the number of times interest is compounded per year. Since it’s compounded monthly, $ n = 12 $.
- $ t $ is the number of years, which is 4.

### Step-by-Step Solution
1. **Convert the monthly rate to annual:** $ r = 0.036 $.
2. **Substitute the values into the formula:**
   \[
   FV = 10000 \left(1 + \frac{0.036}{12}\right)^{12 \times 4}
   \]
3. **Calculate inside the parentheses:**
   \[
   FV = 10000 \left(1 + 0.003\right)^{48}
   \]
4. **Calculate the exponent:**
   \[
   FV = 10000 \times (1.003)^{48}
   \]
5. **Compute the final value.**

Let me perform the calculation.The future value $ FV $ of the investment, compounded monthly at a 0.3% monthly interest rate over 4 years, is approximately **$11,546.35**.

Would you like more details on any of the steps?

Here are some related questions you might explore:
1. How would the future value change if the investment duration was increased to 5 years?
2. What happens to the future value if the compounding frequency changes to quarterly?
3. How would a different principal amount, say $20,000, affect the future value?
4. How does a higher interest rate, such as 0.5% per month, impact the investment’s future value?
5. What is the effect of continuous compounding on the future value compared to monthly compounding?

**Tip:** In compound interest calculations, even small changes in the interest rate or compounding frequency can lead to significant differences in the future value.

Calculate, to the nearest cent, the future value FV of an investment of $10,000 at the stated interest rate after the stated amount of time. 0.3% per month, compounded monthly, after 4 years.

Learn how to calculate the future value (FV) of a $10,000 investment at a monthly interest rate of 0.3%, compounded monthly, over a 4-year period. This example covers key finance concepts, including compound interest, exponential growth, and provides a step-by-step solution suitable for students in Grades 10-12.

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