Try Again Your answer is incorrect. A bank offers an investment account with an annual interest rate of \( 1.13 \% \) compounded quarterly. Charmaine invests \( \$ 3700 \) into the account for 2 years. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Assuming no withdrawals are made, how much money is in Charmaine's account after 2 years? (b) How much interest is earned on Charmaine's investment after 2 years? \( \$ \square \)

To solve these questions, we use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] 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, and \( t \) is the number of years the money is invested for. Given: - \( P = 3700 \) - \( r = 1.13\% = 0.0113 \) - \( n = 4 \) (quarterly) - \( t = 2 \) (a) Plugging in these values: \[ A = 3700 \left(1 + \frac{0.0113}{4}\right)^{4 \cdot 2} \] Calculating this gives: \[ A = 3700 \left(1 + 0.002825\right)^{8} \] \[ A = 3700 \left(1.002825\right)^{8} \] Calculating \( (1.002825)^{8} \) gives approximately \( 1.022868 \). Therefore: \[ A \approx 3700 \times 1.022868 \approx 3785.82 \] So, after rounding to the nearest cent, the amount in Charmaine's account after 2 years is approximately: **\( \$3785.82 \)** (b) To find the interest earned, subtract the principal from the total amount: \[ \text{Interest} = A - P = 3785.82 - 3700 = 85.82 \] Thus, the interest earned on Charmaine's investment after 2 years is approximately: **\( \$85.82 \)**