To help pay for college, Lucy borrowed money from an online lending company. She took out a personal, amortized loan for \( \$ 57,000 \), at an interest rate of \( 5.15 \% \), with monthly payments for a term of 10 years. For each part, 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) Find Lucy's monthly payment. (b) If Lucy pays the monthly payment each month for the full term, find her total amount to repay the loan. \( \$ \square \) (c) If Lucy pays the monthly payment each month for the full term, find the total amount of interest she will pay. \( \$ \square \)

To find Lucy's monthly payment, we can use the formula for an amortized loan: \[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \] Where: \( M \) is the total monthly payment, \( P \) is the loan principal (\$57,000), \( r \) is the monthly interest rate (annual rate/12), and \( n \) is the number of payments (loan term in months). First, convert the annual interest rate to a monthly rate: \( r = \frac{5.15\%}{100} \div 12 \approx 0.00429167 \) Next, determine \( n \): \( n = 10 \times 12 = 120 \) months. Now substitute into the formula: \[ M = 57000 \frac{0.00429167(1 + 0.00429167)^{120}}{(1 + 0.00429167)^{120} - 1} \] Calculating this will yield Lucy's monthly payment. After performing the calculations, you'll find: (a) \( M \approx 608.27 \) To calculate the total amount to repay the loan, multiply the monthly payment by the number of payments: (b) Total Repayment = \( 608.27 \times 120 = 72992.40 \) Finally, for the total interest, subtract the principal from the total repayment: (c) Total Interest = \( 72992.40 - 57000 = 15992.40 \) So the values are: (a) \( \$ 608.27 \) (b) \( \$ 72992.40 \) (c) \( \$ 15992.40 \)