Amy recelved a \( \$ 2100 \) bonus. She decided to invest it in a 5 -year certificate of deposit (CD) with an annual interest rate of \( 1.49 \% \) 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 Amy's account after 5 years? (b) How much interest is earned on Amy's investment after 5 years? \( 5 \square \)

To solve this problem, we will 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 (initial investment). - \( r \) is the annual interest rate (in decimal form). - \( n \) is the number of times the interest is compounded per year. - \( t \) is the time the money is invested for in years. Given: - \( P = \$2100 \) - \( r = 1.49\% = 0.0149 \) (in decimal form) - \( n = 4 \) (compounded quarterly) - \( t = 5 \) years (a) To find the amount of money in Amy's account after 5 years, we substitute the given values into the formula: \[ A = 2100 \left( 1 + \frac{0.0149}{4} \right)^{4 \cdot 5} \] Now, we can calculate the value of \( A \) using the formula. Calculate the value by following steps: - step0: Calculate: \(2100\left(1+\frac{0.0149}{4}\right)^{4\times 5}\) - step1: Divide the terms: \(2100\left(1+\frac{149}{40000}\right)^{4\times 5}\) - step2: Add the numbers: \(2100\left(\frac{40149}{40000}\right)^{4\times 5}\) - step3: Multiply the numbers: \(2100\left(\frac{40149}{40000}\right)^{20}\) - step4: Simplify: \(2100\times \frac{40149^{20}}{40000^{20}}\) - step5: Rewrite the expression: \(100\times 21\times \frac{40149^{20}}{40000^{20}}\) - step6: Rewrite the expression: \(100\times 21\times \frac{40149^{20}}{10000^{20}\times 4^{20}}\) - step7: Rewrite the expression: \(100\times 21\times \frac{40149^{20}}{100^{40}\times 4^{20}}\) - step8: Reduce the numbers: \(21\times \frac{40149^{20}}{100^{39}\times 4^{20}}\) - step9: Multiply the fractions: \(\frac{21\times 40149^{20}}{100^{39}\times 4^{20}}\) The amount of money in Amy's account after 5 years is approximately $2262.11. (b) To find the interest earned on Amy's investment after 5 years, we subtract the initial investment from the final amount: \[ \text{Interest} = A - P \] Substitute the values: \[ \text{Interest} = 2262.11 - 2100 \] Now, we can calculate the interest earned. Calculate the value by following steps: - step0: Calculate: \(2262.11-2100\) - step1: Subtract the numbers: \(162.11\) The interest earned on Amy's investment after 5 years is $162.11.