Part 2 of 3 Which investment results in the greatest total amount? Investment \( \mathrm{A}: \$ 4,000 \) invested for 6 years compounded semiannually at \( 6 \% \). Investment B: \( \$ 6,000 \) invested for 4 years compounded quarterly at \( 2.7 \% \). Find the total amount of investment \( A \). \( \$ 5,703.04 \) (Round to the nearest cent as needed.) Find the total amount of investment B. \( \$ \square \) (Round to the nearest cent as needed.)

To find the total amount of Investment B, we can use the compound interest 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 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 or borrowed. For Investment B: - \( P = 6,000 \) - \( r = 0.027 \) (2.7% as a decimal) - \( n = 4 \) (compounded quarterly) - \( t = 4 \) Now plug in the values: \[ A = 6000 \left( 1 + \frac{0.027}{4} \right)^{4 \cdot 4} \] \[ A = 6000 \left( 1 + 0.00675 \right)^{16} \] \[ A = 6000 \left( 1.00675 \right)^{16} \] Calculating \( (1.00675)^{16} \): \[ (1.00675)^{16} \approx 1.112142 \] Now calculate \( A \): \[ A \approx 6000 \cdot 1.112142 \approx 6672.85 \] Therefore, the total amount of Investment B is: \[ \$ 6,672.85 \] (rounded to the nearest cent as needed).