A homeowner could take out a 15-year mortgage at a 5.5 percent annual rate on a $195,000 mortgage amount, or she could finance the purchase with a 30-year mortgage at a 6.1 percent annual rate. How much total interest over the entire mortgage period could she save by financing her home with the 15-year mortgage (to the nearest dollar)?

The amount of total interest over the entire mortgage period could she save by financing her home with the 15-year mortgage is $138,612

Explanation:

First find the total interest on the 30-year mortgage:

PV = 195,000

N = 360

FV = 0

I = 6.1/12 = 0.5083

195,000 = PMT × PVIFA (0.061/12, 360 months); (in excel)

PMT of 1,181.69 × 360 = 230,408;

Next find the total interest on the 15-year mortgage:

PV = 195,000

N = 180

FV = 0

I = 5.5/12 = 0.4583

195,000 = PMT × PVIFA (0.055/12, 180 months); (in excel)

PMT of 1,593.31 × 180 = 91,796;

The amount of interest saved is: $230,408.34 − $91,796.29 = $138,612.05

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