Tony is taking out a mortgage for \( \$ 152,000 \) to buy a new house and is deciding between the offers from two lende He wants to know which one would be the better deal over the life of the mortgage loan, and by how much. Answer each part. Do not round intermediate computations, and round your answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) A savings and loan association has offered him a 15 -year mortgage loan at an annual interest rate of \( 6.4 \% \). Find the monthly payment. s \( \$ \) A bank has offered him a 40 -year mortgage loan at an annual interest rate of \( 2.4 \% \). (b) the monthly payment. Find then (c) Suppose Tony pays the monthly payment each month for the full term. Which lender's mortgage loan would have the lowest total amount to pay off, and by how much? Savings and loan association The total amount paid would be \( \$ \square \) less than to the bank. Bank The total amount paid would be \( \$ \square \) less than to the savings and loan association.

To find the monthly payments for both offers, we can use the formula for calculating monthly mortgage payments: \[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \] where: - \( M \) = monthly payment - \( P \) = principal amount (loan amount) - \( r \) = monthly interest rate (annual rate divided by 12) - \( n \) = total number of payments (loan term in months) ### (a) Savings and Loan Association Offer For the savings and loan association: - \( P = 152,000 \) - Annual interest rate = 6.4% → \( r = \frac{6.4}{100} / 12 = 0.00533333 \) - Term = 15 years → \( n = 15 \times 12 = 180 \) Plugging in the values: \[ M = 152,000 \frac{0.00533333(1+0.00533333)^{180}}{(1+0.00533333)^{180} - 1} \] Calculating this results in: \[ M \approx 1,072.62 \] Thus, the monthly payment for the savings and loan association is **$1,072.62**. ### (b) Bank Offer For the bank: - \( P = 152,000 \) - Annual interest rate = 2.4% → \( r = \frac{2.4}{100} / 12 = 0.002 \) - Term = 40 years → \( n = 40 \times 12 = 480 \) Using the formula again: \[ M = 152,000 \frac{0.002(1+0.002)^{480}}{(1+0.002)^{480} - 1} \] Calculating this gives: \[ M \approx 613.16 \] Thus, the monthly payment for the bank is **$613.16**. ### (c) Total Payment Over the Life of the Loan Total payment for savings and loan association over 15 years: \[ \text{Total} = M \times n = 1072.62 \times 180 \approx 193,097.60 \] Total payment for the bank over 40 years: \[ \text{Total} = M \times n = 613.16 \times 480 \approx 293,916.80 \] Now, comparing the total payments: - The savings and loan association payment is approximately **$193,097.60** for the full term. - The bank payment is approximately **$293,916.80** for its term. Calculating the difference: \[ 293,916.80 - 193,097.60 = 100,819.20 \] Hence, the savings and loan association’s mortgage loan would result in a total amount paid that is **$100,819.20** less than that of the bank.