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Thread: Problem Flipping/Inverting Mortgage Formula

  1. #1

    Problem Flipping/Inverting Mortgage Formula

    Hi Forum,

    I would really appreciate your help. I have a formula here that calculates the monthly payment amount for a loan:

    P = ( r * A ) / ( 1 - (1+r)-N)

    With: P=Payment Amount, r=Rate of Interest, A=Loan Amount, N=Number of Payments <not that this information is necessary to do the maths

    However I need to find the value of N and I am really struggling in how to flip the formula to get that. I could do it if it was just multiply and divide but the negative power to is really driving me crazy. If you could show me how you did it that would be really helpful also. Thanks in advance!

  2. #2
    Elite Member
    Join Date
    Feb 2004
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    Ottawa, Ontario
    Posts
    17,062
    Quote Originally Posted by mishaelsmith View Post
    P = ( r * A ) / ( 1 - (1+r)-N)
    So, to isolate N:

    Rule: a^(-p) = 1 / a^p ; forgot that?

    Let k = (1+r) ; save typing!

    P = Ar / (1 - k^(-N))

    P = Ar / (1 - 1/k^N)

    Ar = P - P/k^N

    P/k^N = P - Ar

    I'll leave you the satisfaction of wrapping it up
    I'm just an imagination of your figment !

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