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31 August, 10:09

Joe Levi bought a home in Arlington, Texas, for $147,000. He put down 25% and obtained a mortgage for 30 years at 8.00%. What is the difference in interest cost if he had obtained a mortgage rate of 6.00%

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  1. 31 August, 11:48
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    53,367

    Explanation:

    The first thing we do is to substract the down payment from the initial amount, because this payment is not part of the mortgage.

    147,000 x 25% = 36,750

    147,000 - 36,750 = 110,250

    Next, to find the financed amount we use the present value of an annuity formula:

    PV = X [ (1 - (1 + i) ^-n) / i ]

    Where:

    PV = Present value, in this case, the initial financed amount of $110,250 X = Value of the annuity payments. i = Interest rate n = number of compounding periods

    For the 8% interest rate we have:

    110,250 = X [ (1 - (1 + 0.08) ^-30) / 0.08]

    110,250 = X [11.26]

    110,250 / 11.26 = X

    9,791.3 = X

    Now we multiply this value by 30 to obtain the total amount paid

    9,791.3 * 30 = 293,739

    The total interest cost under then 8% interest rate is the total amound paid minus the initial amount:

    Total interest cost = 293,739 - 110,250

    = 183,489

    We do the same for the 6% interest rate:

    110,250 = X [ (1 - (1 + 0.06) ^-30) / 0.06]

    110,250 = X [13.76]

    110,250 / 13.76 = X

    8,012.4 = X

    8,012.4 * 30 = 240,372

    Total interest cost = 240,372 - 110,250

    = 130,122

    Difference in interest cost = 183,489 - 130,122

    = 53,367
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