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28 July, 00:33

The monthly mortgage payment on your house is $821.69. it is a 30 year mortgage at 6.5% compounded monthly. how much did you borrow?

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  1. 28 July, 03:05
    0
    To find present value from monthly payments, we use

    P_A=A ((1+i) ^n-1) / (i (1+i) ^n)

    where

    A=monthly payment = $821.69

    i=monthly interest rate = 6.5%/12 = 0.065/12

    n=number of months = 30*12 = 360

    Therefore

    Present value

    = amount borrowed

    =A ((1+i) ^n-1) / (i (1+i) ^n)

    =821.69 * ((1+0.065/12) ^360-1) / ((0.065/12) * (1+0.065/12) ^360)

    = 130000.25

    (note: the 0.25 could well be a round off error because the monthly payment is only accurate to the cent)
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