If 33900 dollars is invested at an interest rate of 8 percent per year, compounded semiannually, find the value of the investment after the given number of years. Round value to the nearest cent. (a) 5 years: Your answer is (b) 10 years: Your answer is (c) 15 years: Your answer is

To find the future value of an investment compounded semiannually, you can use the formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial sum of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the time the money is invested for in years. Here, \( P = 33900 \), \( r = 0.08 \), and \( n = 2 \) (since interest is compounded semiannually). (a) For 5 years: \[ A = 33900 \left(1 + \frac{0.08}{2}\right)^{2 \cdot 5} = 33900 \left(1 + 0.04\right)^{10} = 33900 \left(1.04\right)^{10} \] Calculating that gives: \[ A \approx 33900 \times 1.48024 \approx 50215.99 \] Your answer is **$50,215.99**. (b) For 10 years: \[ A = 33900 \left(1 + \frac{0.08}{2}\right)^{2 \cdot 10} = 33900 \left(1 + 0.04\right)^{20} = 33900 \left(1.04\right)^{20} \] Calculating that gives: \[ A \approx 33900 \times 2.20899 \approx 74726.67 \] Your answer is **$74,726.67**. (c) For 15 years: \[ A = 33900 \left(1 + \frac{0.08}{2}\right)^{2 \cdot 15} = 33900 \left(1 + 0.04\right)^{30} = 33900 \left(1.04\right)^{30} \] Calculating that gives: \[ A \approx 33900 \times 3.24340 \approx 109,228.73 \] Your answer is **$109,228.73**.