Felipe received a \( \$ 1200 \) bonus. He decided to invest it in a 3 -year certificate of deposit (CD) with an annual interest rate of \( 1.27 \% \) compounded quarterly. 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 Felipe's account after 3 years? (b) How much interest is earned on Felipe's investment after 3 years? \( \$ \square \)

To solve this problem, we can use the formula for compound interest, which is given by: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] 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 time the money is invested for in years. Given: - \( P = 1200 \) - \( r = 0.0127 \) - \( n = 4 \) (quarterly compounding) - \( t = 3 \) Plugging the values into the formula: \[ A = 1200 \left(1 + \frac{0.0127}{4}\right)^{4 \times 3} \] Calculating each part step by step: 1. Calculate \( \frac{0.0127}{4} = 0.003175\) 2. Calculate \( 4 \times 3 = 12\) 3. Calculate \( (1 + 0.003175)^{12} \approx (1.003175)^{12} \approx 1.038672\) 4. Then multiply by \( 1200 \): \[ A \approx 1200 \times 1.038672 \approx 1246.42 \] (a) After 3 years, the amount in Felipe's account is approximately \( \$1246.42 \). To find the interest earned on Felipe's investment, we can simply subtract the principal from the total amount: \[ \text{Interest} = A - P = 1246.42 - 1200 = 46.42 \] (b) Thus, the interest earned on Felipe's investment after 3 years is \( \$46.42 \).