Question

A loan officer states, "Thousands of dollars can be saved by switching to a 15-year mortgage from a 30-year mortgage." Calculate the difference in payments on a 30-year mortgage at an interest of 0.75% a month versus a 15-year mortgage with an interest rate of 0.7% a month. Both mortgage are for $100,000 and have monthly payments.

1) What is the monthly payment committed by the 30-year mortgage? And the total payment?

2) What is the monthly payment committed by the 15-year mortgage? And the total payment?

3) What is the difference in total dollars that will be paid to the lender under each loan?

Answer 1

1. Let the monthly payment be A. So, writing the PV equation, we have:
100000 = A x (1/1.0075 + 1/1.0075^2 + ... + 1/1.0075^360)

A = 804.6226.

Hence, the total payment will be = 804.6226 x 360 = $289,664.1

2. Let the monthly payment be A. So, writing the PV equation, we have:
100000 = A x (1/1.007 + 1/1.007^2 + ... + 1/1.007^180)

A = 978.886.

Hence, the total payment will be = 978.886 x 180 = $176,199.6

3. Hence, the difference in dollars is 289664.1 - 176199.6 = $113464.5 (with the 15-year payment being a better option)

answered by: anonymous