MATH

Dave takes out a 24-year mortgage of 210,000 dollars for his new house. Dave gets an interest rate of 13.2 present compounded monthly. He agreed to make equal monthly payment, the first coming in one month. After making the 68th payment, Dave wants to buy a boat, so he wants to refinance his house to reduce his monthly payment by 500 dollars, and to get a better interest rate. In particular, he negotiates a new rate of 7.2 percent compounded monthly, and agress to make equal monthly payments (each 500 dollars less than his orginal payments) for as long as necessary, followed by a single smaller payment. How large will Dave's final loan payment be?

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  1. original loan:
    payment -- p
    i = .132/12 = .011
    n = 288
    PV = 21000
    p( 1 - 1.011^-288)/.011 = 210000
    I got p = $2413.34

    balance after 68th payment
    = 210000(1.011^87) - 2413.34(1.011^87 - 1)/.011
    = $195,059.83

    new payment - 2413.3-500 = 1913.34
    new i = .072/12 = .006
    PV = 195059.83
    n = ??

    1913.34( 1 - 1.006^-n)/.006 = 195059.83
    1 - 1.006^-n = .061168374
    1.006^-n = .388316259
    using logs
    -n log 1.006 = log .388316259
    -n = -158.128
    n = 158.128

    So 158 full payments plus a partial payment are needed.

    Your turn:
    find the outstanding balance after 158 payments following the same steps I used above.
    Find the interest on the remaining balance by multiplying it by .006, add that to the outstanding balance you just found and you got it.

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  2. 98

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