Your banker suggests that, rather than obtaining a $90,000 mortgage over 25-years, you should simply obtain a 15-year loan for the same amount. The rate on this loan is 7.75% compounded monthly. By how much will your monthly payment be (higher/lower) for the 15-year loan than the regular payment on the 25-year loan?

Question

Quizplus · Accepted Answer

To determine the monthly payment difference, we calculate the monthly payments for both the 25-year and 15-year loans using the formula for a fixed-rate mortgage. The monthly payment formula is P = [r*PV] / [1 - (1 + r)^-n], where P is the monthly payment, r is the monthly interest rate (annual rate/12), PV is the loan amount, and n is the total number of payments (years*12). For the 25-year loan at 7.75% annual interest, the monthly interest rate is 0.0775/12. For the 15-year loan, it's the same rate but with fewer payments. Calculating both and subtracting the 25-year payment from the 15-year payment gives the difference, which is higher for the 15-year loan due to the shorter term, leading to higher monthly payments but less interest paid over the life of the loan.

Your Banker Suggests That, Rather Than Obtaining a $90,000 Mortgage