TheMortgageReports.com reported the median price of a home sold in the United States hit a record high in 2020 at just above $\$ 320,000$. Juan Carlos Soto, Jr., wants to purchase a new home for $\$ 330,500$. Juan puts $20 \%$ down and will finance the remainder of the purchase. Compare the following two mortgage options he has: 15 years at $3.5 \%$ or 20 years at $7.0 \%$. (Use Table 15.1.) Note: Round your intermediate calculations and final answers to the nearest cent. a. Calculate Juan's monthly payment for both the 15 and 20 year mortgage? \begin{tabular}{|l|l|} \hline Monthly payment for 15 year mortgage & \\ \hline Monthly payment for 20 year mortgage & \\ \hline \end{tabular} b. Calculate Juan's total cost of interest for both the 15 and 20 year mortgage? \begin{tabular}{|l|l|} \hline Total cost of interest for 15 year mortgage \\ \hline Total cost of interest for 20 year mortgage \\ \hline \end{tabular} c. What is the difference in interest paid between 15 and 20 year mortgage? Difference in interest paid Prev 9 of 9 Next
Solution
Step 1 ：\(\text{Amount to finance} = 330,500 \times 0.80 = 264,400\)
Step 2 ：\(\text{For the 15 year mortgage at 3.5%:}\)
Step 3 ：\(r = \frac{3.5}{12} = 0.002917\)
Step 4 ：\(n = 15 \times 12 = 180\)
Step 5 ：\(P = \frac{0.002917 \times 264,400}{1 - (1 + 0.002917)^{-180}} = 1,889.70\)
Step 6 ：\(\text{For the 20 year mortgage at 7.0%:}\)
Step 7 ：\(r = \frac{7.0}{12} = 0.005833\)
Step 8 ：\(n = 20 \times 12 = 240\)
Step 9 ：\(P = \frac{0.005833 \times 264,400}{1 - (1 + 0.005833)^{-240}} = 2,056.61\)
Step 10 ：\(\text{For the 15 year mortgage:}\)
Step 11 ：\(\text{Total payments} = 1,889.70 \times 180 = 340,146\)
Step 12 ：\(\text{Total interest} = 340,146 - 264,400 = 75,746\)
Step 13 ：\(\text{For the 20 year mortgage:}\)
Step 14 ：\(\text{Total payments} = 2,056.61 \times 240 = 493,586.40\)
Step 15 ：\(\text{Total interest} = 493,586.40 - 264,400 = 229,186.40\)
Step 16 ：\(\text{Difference in interest paid} = 229,186.40 - 75,746 = \boxed{153,440.40}\)
