Use the formula for computing future value using compound interest to determine the value of an account at the end of 8 years if a principal amount of \( \$ 5,000 \) is deposited in an account at an annual interest rate of \( 3 \% \) and the interest is compounded monthly.

To find the future value of the account, we can use the compound interest formula: \[ FV = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \( FV \) is the future value, - \( P \) is the principal amount (\$5,000), - \( r \) is the annual interest rate (0.03), - \( n \) is the number of times interest is compounded per year (12 for monthly), - \( t \) is the number of years the money is invested (8 years). Plugging the values into the formula: \[ FV = 5000 \left(1 + \frac{0.03}{12}\right)^{12 \times 8} \] Calculating it step by step: 1. Calculate \( \frac{r}{n} = \frac{0.03}{12} = 0.0025 \) 2. Find \( nt = 12 \times 8 = 96 \) 3. Now plug these values back into the equation: \[ FV = 5000 \left(1 + 0.0025\right)^{96} = 5000 \left(1.0025\right)^{96} \] Calculating \( (1.0025)^{96} \approx 1.2505 \): Now, multiply by the principal: \[ FV \approx 5000 \times 1.2505 \approx 6252.50 \] Therefore, the value of the account at the end of 8 years will be approximately \( \$6,252.50 \). Now that's quite the payday!