1. The problem is to calculate the future value (FV) of an investment using the formula: $$FV = P \left[ \frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}} \right]$$ where: - $P$ is the payment amount per period, - $r$ is the annual interest rate, - $n$ is the number of compounding periods per year, - $t$ is the number of years. 2. Given values are $P = 100$, $r = 0.076$, $n = 12$, and $nt = 60$ (which implies $t = 5$ years). 3. Calculate the monthly interest rate: $$\frac{r}{n} = \frac{0.076}{12} = 0.0063333...$$ 4. Calculate the term inside the exponent: $$nt = 60$$ 5. Calculate the compound factor: $$\left(1 + 0.0063333...\right)^{60} = (1.0063333...)^{60}$$ Using a calculator, this is approximately: $$1.0063333^{60} \approx 1.42576$$ 6. Substitute back into the formula: $$FV = 100 \left[ \frac{1.42576 - 1}{0.0063333} \right] = 100 \left[ \frac{0.42576}{0.0063333} \right]$$ 7. Calculate the fraction: $$\frac{0.42576}{0.0063333} \approx 67.19$$ 8. Finally, calculate the future value: $$FV = 100 \times 67.19 = 6719$$ So, the future value of the investment is approximately 6719.