Ali received a \( \$ 2100 \) bonus. He decided to invest it in a 5 -year certificate of deposit (CD) with an annual interest rate of \( 1.44 \% \) 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 Ali's account after 5 years? (b) How much interest is earned on Ali's investment after 5 years? \( \$ \square \)

To solve Ali's investment 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 (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. Given: - \( P = 2100 \) - \( r = 0.0144 \) (which is \( 1.44\% \) as a decimal) - \( n = 4 \) (since interest is compounded quarterly) - \( t = 5 \) (a) Calculate the total amount after 5 years: \[ A = 2100 \left(1 + \frac{0.0144}{4}\right)^{4 \times 5} \] Calculating within the parentheses: \[ \frac{0.0144}{4} = 0.0036 \] Thus, \[ A = 2100 \left(1 + 0.0036\right)^{20} \] Calculating inside the parentheses: \[ 1 + 0.0036 = 1.0036 \] Now, raise it to the power of 20: \[ A = 2100 \times (1.0036)^{20} \] Calculating \( (1.0036)^{20} \): \[ (1.0036)^{20} \approx 1.07512 \] Now calculate \( A \): \[ A \approx 2100 \times 1.07512 \approx 2257.18 \] So, after 5 years, the amount in Ali's account is approximately \( \$2257.18 \). (b) To find out how much interest is earned on Ali's investment after 5 years, subtract the principal from the total amount: \[ \text{Interest} = A - P \] \[ \text{Interest} = 2257.18 - 2100 = 157.18 \] Thus, the total interest earned is approximately \( \$157.18 \). Final answers: (a) \( \$ 2257.18 \) (b) \( \$ 157.18 \)