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Math Help - Strange Loan

  1. #1
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    Strange Loan

    Jack borrows $A, over 15 months, at interest of 12% compounded monthly: 1% per month.

    For the first 5 months, payment will be 10% of balance owing.
    As example, if $3000 borrowed, 1st payment will be $300,
    resulting in balance owing of 3000 - 300 + 30 = 2730;
    so the next payment will be .10(2730) = $273,
    resulting in balance owing of 2730 - 273 + 27.30 = 2484.30

    For the remaining 10 months, the monthly payment will be constant
    at $50 per month: the 10th $50 payment will result in a zero balance owing.

    How much did Jack borrow?
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  2. #2
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    Owing at month 15: $0.00
    Owing at month 14: 50/1.01 = 49.50495
    Owing at month 13: (49.50495+50)/1.01 = 98.51975
    etc...
    Owing at month 5: 473.5652
    Month 5 Consideration: (473.5652 + q*0.1)/1.01 = q
    Owing at Month 4: q
    etc...

    Alternatively:

    Borrowed: A
    To Be Paid in Month 1: 0.1*A
    Owing at Month A: A*1.01 - 0.1*A = 0.91*A

    It's relatively straight-forward. If nothing else, a spreadsheet makes a very good tool for some problems.
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  3. #3
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    Ya; but more fun to work out a general case formula:

    p = .10, i = .01, m = 50, x = 5, y = 10

    A = m(j - 1) / (i j k)
    where:
    j = (1 + i)^y
    k = (1 + i - p)^x
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  4. #4
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    More fun that THREE different ways? I think not.

    In any case, glad to see #4.
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