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Math Help - Stranger loan

  1. #1
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    Stranger loan

    AcmeCard works like this:
    monthly payments = fixed percentage of balance owing before interest is added,
    with minimum payment specified; interest is charged monthly.

    Example: $1000 owing, payment = 7% of balance owing, mimimum payment = $50, interest 1% per month.

    Month1: 1000.00 - 70.00 + 10.00 = 940.00
    Month2: 940.00 - 65.80 + 9.40 = 883.60

    Month6 ends with ~689.87 owing; minimum payment starts in month7, since 689.87 * .07 = ~48.29

    Month20 will end at ~45.62, lesser than minimum payment of 50.
    So FINAL payment will be in month21, for 45.62(1.01) = ~46.08

    Clear nuff?

    OK:
    a = original amount owing (1000 in above)
    i = monthly interest factor (.01 in above)
    p = percent of balance factor (.07 in above)
    m = minimum payment (50 in above)

    As a "general case", what is the FINAL payment in terms of a,i,p,m ?

    Of course, it is assumed that at least the 1st payment is higher than the minimum payment.
    In other words, ap > m.
    Last edited by Wilmer; August 29th 2009 at 07:36 AM. Reason: none
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