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Math Help - min repayment

  1. #1
    da`
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    min repayment

    hello,

    i am struggling a wee bit trying to find a formula that is behind this calculator

    Minimum Repayments: DANGER! Don't get locked into debt....

    it can be found by scrolling half way down.

    the problem for me is the minimum for choosing say 3% or 10 in payments.

    any help would be really appreciated

    thanks
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  2. #2
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    Don't understand what you're asking.

    That calculator works fine.
    I entered 1000 balance, interest of 1% per month,
    payments of 2% of outstanding balance with 5 minimum, and got:
    17 years 4 months, total cost of 848; which is exactly correct.

    Opening balance owing: 1000.00
    1st month: -20.00 +10.00 990.00
    2nd month: -19.80 +9.90 980.10
    and so on....
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  3. #3
    da`
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    Hi Wilmer,

    I am wondering if there is just one formula that could summarise this calculator without having to do the iterative method. I am creating a calculator similar to this for a website.

    Thanks alot
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  4. #4
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    Take this example:
    a = amount owing ; 1000
    i = interest monthly ; .01
    p = percentage payment ; .03
    m = mimimum payment ; 15

    Can be treated as a saving account receiving negative interest (thus being depleted)
    at rate of (p - i)%, or $1000 at rate -.02 per month in above example.
    1000 - 20 = 980; 980 - 19.60 = 960.40; and so on...

    Required is calculation of the month where the balance owing is such
    that a switch to the minimum payment is required.
    In other words, ap(1 + i - p)^n = m ; solving for n, and converting to integer:
    n = INT{LOG[m / (ap)] / LOG(1 + i - p)} + 1

    For above example, you'll get n = 35.
    Actually, at month 35, ~493.07 is owing.
    493.07 * .03 = 14.79 ; hence the switch to minimum payment of 15.

    Let k = 1 - i + p (less typing!)
    The amount owing of 493.07 obtained from: ak^n

    Now required is the number of minimum payments of $15 that'll pay off this 493.07.
    Obtained from formula m = [a i k^n] / [1 - 1 / (1 + i)^x]
    The x is the number of months left; solving for x:
    x = LOG[m / (m - a i k^n)] / LOG[1 + i]
    Here you'll get x = 40.055....; means a partial 41st payment.
    Actual balance owing after 40th minimum payment is .83 only.

    So you'd round out the x to: INT(x) + 1

    Now we have the number of months for the whole thing: n + x = 35 + 41 = 76

    As far as the interest cost goes, I'm not sure that it can be calculated
    by formula, or as a derivative of the above formulas.
    I don't think it can...so iterative process required.
    But I see nothing wrong with having such a process in a calculator:
    most respectable calculators do!

    Don't despair: perhaps someone else will come up with a direct way...
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  5. #5
    da`
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    Quote Originally Posted by Wilmer View Post
    a = amount owing ; 1000
    i = interest monthly ; .01
    p = percentage payment ; .03
    m = mimimum payment ; 15


    Required is calculation of the month where the balance owing is such
    that a switch to the minimum payment is required.
    In other words, ap(1 + i - p)^n = m ; solving for n, and converting to integer:
    n = INT{LOG[m / (ap)] / LOG(1 + i - p)} + 1

    For above example, you'll get n = 35.
    Actually, at month 35, ~493.07 is owing.
    493.07 * .03 = 14.79 ; hence the switch to minimum payment of 15.
    Sorry. I have tried a few times to get 35 from that formula you gave but i am getting other values

    Quote Originally Posted by Wilmer View Post
    Now required is the number of minimum payments of $15 that'll pay off this 493.07.
    Obtained from formula m = [a i k^n] / [1 - 1 / (1 + i)^x]
    The x is the number of months left; solving for x:
    x = LOG[m / (m - a i k^n)] / LOG[1 + i]
    Here you'll get x = 40.055....; means a partial 41st payment.
    Actual balance owing after 40th minimum payment is .83 only.

    So you'd round out the x to: INT(x) + 1
    and again I am not getting 40.055.... for this one?

    can you show me how you gain those values?

    Thanks alot
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  6. #6
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    Dunno what to tell you, dada.
    Are you using a calculator?
    How would I know why you're not getting those answers?
    You're obviously coding something improperly.

    n = INT{LOG[m / (ap)] / LOG(1 + i - p)} + 1

    =INT{[LOG(15 / 30)] / LOG(.98)} + 1
    = 35
    Last edited by Wilmer; September 1st 2009 at 03:58 PM. Reason: none
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