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The problem asks to calculate the future value (FV) of an investment using the given information:

- Initial investment (PV): $400
- Time period: 2 years
- Interest rate: 5% per year (compounded annually)

### Formula for Future Value with Compound Interest:
\[
FV = PV \times (1 + \frac{r}{n})^{nt}
\]
Where:
- $ PV $ = Present Value ($400)
- $ r $ = Annual interest rate (5% or 0.05)
- $ n $ = Number of times interest is compounded per year (since it's compounded annually, $ n = 1 $)
- $ t $ = Time the money is invested (2 years)

### Step-by-Step Calculation:
1. The interest is compounded annually, so $ n = 1 $.
2. Plug in the values:
\[
FV = 400 \times (1 + \frac{0.05}{1})^{1 \times 2}
\]
\[
FV = 400 \times (1.05)^2
\]
3. Calculate $ (1.05)^2 = 1.1025 $.
4. Multiply:
\[
FV = 400 \times 1.1025 = 441
\]

### Future Value (FV):
The accumulated value after 2 years will be **$441**.

Would you like more details or have any other questions? 

Here are 5 related questions you can explore:
1. How does increasing the interest rate affect the future value?
2. What happens if the interest is compounded monthly instead of annually?
3. How does extending the investment period to 5 years change the future value?
4. What is the difference between simple and compound interest?
5. How would the result change if the initial investment were $1000?

**Tip:** Compounding more frequently increases the accumulated future value because interest is calculated and added more often.

Invested $400 for 2 years at 5% compounded annually. Calculate the accumulated value (i.e., Future Value).

Learn how to calculate the future value of $400 invested for 2 years at an annual compound interest rate of 5%. This problem covers key financial math concepts, including compound interest formulas. Suitable for high school students (Grades 9-12).

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