1. **Problem Statement:** Calculate the accumulated value (Future Value) of an investment of $400 with an interest rate of 5% compounded $N$ times over a certain time period. 2. **Formula Used:** The Future Value (FV) formula for compound interest is: $$FV = PV \times \left(1 + \frac{i}{N}\right)^{N \times t}$$ where: - $PV$ is the present value (initial investment), here $400$ - $i$ is the annual interest rate (decimal), here $0.05$ - $N$ is the compounding frequency per year - $t$ is the time in years 3. **Given:** - $PV = 400$ - $i = 0.05$ - $N$ and $t$ are not explicitly given, so we cannot calculate a numeric FV without these values. 4. **Explanation:** To find the accumulated value, you need to know how many times the interest is compounded per year ($N$) and the total number of years ($t$). The total number of compounding periods is $N \times t$. 5. **If $N$ and $t$ were given, for example $N=12$ (monthly) and $t=5$ years, then: $$FV = 400 \times \left(1 + \frac{0.05}{12}\right)^{12 \times 5}$$ 6. **Intermediate step:** $$FV = 400 \times \left(1 + 0.0041667\right)^{60} = 400 \times (1.0041667)^{60}$$ 7. **Calculate:** $$FV = 400 \times 1.28368 = 513.47$$ 8. **Final answer:** The accumulated value after 5 years with monthly compounding at 5% interest is approximately $513.47$. **Note:** Without specific values for $N$ and $t$, the exact FV cannot be calculated.