Mortgage Bankers Association reported the median price of a home sold in the Uni

Question

Mortgage Bankers Association reported the median price of a home sold in the United States in January 2015 was $199,600. Pat Radigan wants to purchase a new home for $310,500. Pat puts 20% down and will finance the remainder of the purchase. Compare the following two mortgage options he has: 10 years at 3.5% or 15 years at 5.0%. (Use Table 15.1). (Round your intermediate calculations and final answers to the nearest cent.) a. Calculate Pat’s monthly payment for both the 10 and 15 year mortgage? Monthly payment for 10 year mortgage $ Monthly payment for 15 year mortgage $ b. Calculate Pat’s total cost of interest for both the 10 and 15 year mortgage? Total cost of interest for 10 year mortgage $ Total cost of interest for 15 year mortgage $ c. What is the difference in interest paid between 10 and 15 year mortgage? Difference $

Explanation / Answer

Hi,
Given the cost of house is 310,500, since 20% is down payment, loan is only needed for 0.80* 310,500 i.e 248400
first option- 10 years at 3.5%
the monthly payment is given by  L[c(1 + c)n]/[(1 + c)n - 1] where L is the loan amount, n is number of months and c is monthly interest rate therfore substituing valuse, we get
248400((0.35/12)(1+(0.35/12))^120)/((1+(0.35/12))^120-1) = $2,456.32
total interest is 46,359
Second option-
15 years at 5%
monthly payment using the same formula is 1,964.33
total interest is 105,180
therfore difference is 105,180- 46,359 =$58821
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