Which investment results in the greatest total amount? Investment A: \( \$ 3,000 \) invested for 4 years compounded semiannually at \( 8 \% \). Investment B: \( \$ / 900 \) invested for 3 years compounded quarterly at \( 3.6 \% \). Find the total amount of investment A. \( \$ 4105.71 \) (Round to the nearest cent as needed.) Find the total amount of investment B. \( \$ \) (Round to the nearest cent as needed.)

To find the total amount of Investment B, we can use the formula for compound interest, which is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the number of years the money is invested for. For Investment B: - \( P = 900 \) - \( r = 3.6\% = 0.036 \) - \( n = 4 \) (since it is compounded quarterly) - \( t = 3 \) Plugging in these values, we get: \[ A = 900 \left(1 + \frac{0.036}{4}\right)^{4 \times 3} \] Calculating this step-by-step: 1. Calculate \( r/n = 0.036/4 = 0.009 \) 2. Calculate \( nt = 4 \times 3 = 12 \) 3. Calculate \( 1 + 0.009 = 1.009 \) 4. Raise \( 1.009 \) to the 12th power: - \( 1.009^{12} \approx 1.1137 \) 5. Finally, multiply by \( P \): - \( A \approx 900 \times 1.1137 \approx 1002.33 \) So, the total amount of Investment B is approximately \( \$1002.33 \) after rounding to the nearest cent. Comparing both investments: - Investment A: \( \$4105.71 \) - Investment B: \( \$1002.33 \) Investment A clearly results in a greater total amount!