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 rate of 1% a month versus a 15-year mortgage with an interest rate of 1.2% a month. Both mortgages are for $100,000 and have monthly payments. What is the difference in total dollars that will be paid to the lender under each loan? (Round the monthly payment amounts to 2 decimal places.)

Answer 1

Monthly payment on 30 year loan is computed as shown below:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

$ 100,000 = Monthly payment x [ (1 - 1 / (1 + 0.01)³⁶⁰ ) / 0.01 ]

$ 100,000 = Monthly payment x 97.21833108

Monthly payment = $ 100,000 / 97.21833108

Monthly payment = $ 1,028.61

So, the total amount will be as follows:

= $ 1,028.61 x 360 months

= $ 370,299.6

Monthly payment on 15 year loan is computed as shown below:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

$ 100,000 = Monthly payment x [ (1 - 1 / (1 + 0.012)¹⁸⁰ ) / 0.012 ]

$ 100,000 = Monthly payment x 73.59854522

Monthly payment = $ 100,000 / 73.59854522

Monthly payment = $ 1,358.72

So, the total amount will be as follows:

= $ 1,358.72 x 180 months

= $ 244,569.6

So, the difference will be as follows:

= $ 370,299.6 - $ 244,569.6

= $ 125,730

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