A bank offers an investment account with an annual interest rate of \( 1.45 \% \) compounded daily. Kaitlin invests \( \$ 3400 \) into the account for 5 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. Assume there are 365 days in each year. (a) Assuming no withdrawals are made, how much money is in Kaitlin's account after 5 years? (b) How much interest is earned on Kaitlin's investment after 5 years?

To solve the problem, we will 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 number of years the money is invested or borrowed. Given: - \( P = 3400 \) - \( r = 1.45\% = 0.0145 \) - \( n = 365 \) (compounded daily) - \( t = 5 \) ### (a) Calculate the amount in Kaitlin's account after 5 years. Substituting the values into the formula: \[ A = 3400 \left(1 + \frac{0.0145}{365}\right)^{365 \times 5} \] Calculating \( \frac{0.0145}{365} \): \[ \frac{0.0145}{365} \approx 0.000039726 \] Now, calculate \( 365 \times 5 = 1825 \). Now we can compute \( A \): \[ A = 3400 \left(1 + 0.000039726\right)^{1825} \] Calculating \( 1 + 0.000039726 \): \[ 1 + 0.000039726 \approx 1.000039726 \] Now we raise this to the power of 1825: \[ A \approx 3400 \times (1.000039726)^{1825} \] Using a calculator to compute \( (1.000039726)^{1825} \): \[ (1.000039726)^{1825} \approx 1.077308 \] Now, calculate \( A \): \[ A \approx 3400 \times 1.077308 \approx 3662.95 \] Thus, the amount in Kaitlin's account after 5 years is approximately: \[ \boxed{3662.95} \] ### (b) Calculate the interest earned on Kaitlin's investment after 5 years. The interest earned can be calculated by subtracting the principal from the total amount: \[ \text{Interest} = A - P \] Substituting the values we have: \[ \text{Interest} = 3662.95 - 3400 = 262.95 \] Thus, the interest earned on Kaitlin's investment after 5 years is approximately: \[ \boxed{262.95} \]