The price of a home is \( \$ 200,000 \). The bank requires a \( 15 \% \) down payment. The buyer is offered two mortgage options: 15 -year fixed at \( 6.5 \% \) or 30 -year fixed at \( 6.5 \% \). Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 15 -year option? Use the following formula to determine the regular payment amount. PMT \( =\frac{\mathrm{P}\left(\frac{\mathrm{r}}{\mathrm{n}}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} \) Find the monthly payment for the 15 -year option. \( \$ 1,481 \) (Round to the nearest dollar as needed.) Find the monthly payment for the 30 -year option. \( \$ 1,075 \) (Round to the nearest dollar as needed.) Calculate the total cost of interest for both mortgage options. How much does the buyer save in interest with the 15 -year option? \( \$ \square \) (Use the answers from parts 1 and 2 to find this answer.)
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To calculate the total cost of interest for both mortgage options, we start by determining the total payments made over the life of each loan. For the 15-year option: - Monthly Payment: \( \$ 1,481 \) - Total Payments Over 15 Years: \( 1,481 \times 12 \times 15 = \$ 266,580 \) - Total Interest Paid: \( 266,580 - (200,000 - 30,000) = 266,580 - 170,000 = \$ 96,580 \) For the 30-year option: - Monthly Payment: \( \$ 1,075 \) - Total Payments Over 30 Years: \( 1,075 \times 12 \times 30 = \$ 387,000 \) - Total Interest Paid: \( 387,000 - (200,000 - 30,000) = 387,000 - 170,000 = \$ 217,000 \) Now, to find the savings in interest with the 15-year option: - Interest Savings: \( 217,000 - 96,580 = \$ 120,420 \) So the total interest cost for the 15-year option is \( \$ 96,580 \), and the savings over the 30-year option is \( \$ 120,420 \).
