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30 May, 17:56

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) ?

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  1. 30 May, 18:22
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    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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