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Math Help - Amortization - LOGS!! Help

  1. #1
    Newbie
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    Sep 2008
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    Amortization - LOGS!! Help

    I'm actually working on an amortization problem.

    I am trying to solve for n. I have all of the other values.

    In order to do this I end up using logs (i think...)

    A/P/r = (1+r) ^n /((1+r)^n - 1)

    Does that turn into something like...

    log[A/P/r] = log[(1+r)^n] - log[(1+r)^n - 1]

    And where do I go from there?!?

    THANKS!!
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    1,631
    You want to solve for n from the
    A = P[r*(1+r)^n] / [(1+r)^n -1].

    Here is one way. The idea is just to isolate n by itself alone on one side of the equation.

    Divide both sides by r*P,
    A / rP = [(1+r)^n] / [(1+r)^n -1]

    Multiply both sides by [(1+r)^n -1],
    [A / rP]*[(1+r)^n -1] = (1 +r)^n

    Expand,
    [A / rP](1+r)^n -[A / Pr] = (1+r)^n

    Collect like terms,
    [A / Pr](1+r)^n -(1+r)^n = [A / Pr]

    (1+r)^n *{[A / Pr] -1} = [A / Pr]
    (1+r)^n = [A / Pr] / {[A / Pr] -1}

    Take the natural logs of both sides,
    n*Ln(1+r) = Ln[A / pr] -Ln{[A / Pr] -1}

    Therefore,
    n = (Ln[A / Pr] -ln{[A / Pr] -1}) / Ln(1+r)
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