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 .75% a month versus a 15-year mortgage with an interest rate of .7% 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?

$113,465

Explanation:

Calculation to determine difference in total dollars that will be paid to the lender under each loan

First step is to Calculate the difference in payments on a 30-year mortgage at an interest rate of .75% a month

$100,000 = PMT([1 / (0.0075)] − 1 / {(0.0075)[(1.0075)]^30 × 12})

PMT = $804.62

Second step is to Calculate the difference in payments on a 15-year mortgage at an interest rate of .7% a month

$100,000 = PMT([1 / (0.007)] − 1 / {(0.007 )[ 1.007)]^15 × 12})

PMT = $ 978.87

Now let determine the Total difference

Total difference = ($804.62 × 12 × 30) − ($978.87 × 12 × 15)

Total difference= $113,465

Therefore difference in total dollars that will be paid to the lender under each loan is $113,465

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