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Annuity Equation isolating n value HELP!

  1. May 4, 2008 #1
    Annuity Equation "isolating n value" HELP!

    [tex]R =\frac{Pi(1+i)^n}{(1+i)^n-1}[/tex]

    1. I need to solve for n.
    • n = number of years
    • P = Investment
    • R = Yearly Savings
    • i = interest rate

    3. My Attempt:

    [tex]R =\frac{Pi(1+i)^n}{(1+i)^n-1}\rightarrow -1 \cdot R = \frac{Pi(1+i)^n}{(1+i)^n} \cdot -1 [/tex]

    Once I get here I'm left with:

    [tex]-R =\frac{Pi(1+i)^n}{(1+i)^n}[/tex]

    It seems like the quantities of [tex](1+i)^n[/tex] cancel so I'm left with:

    [tex]R = Pi[/tex]

    I know this isn't correct, and I've tried it many other ways with no luck.

    Any help would be greatly appreciated!
    Last edited: May 4, 2008
  2. jcsd
  3. May 4, 2008 #2


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    Welcome to PF!

    Hi LordofDirT ! Welcome to PF! :smile:

    (nice LaTeX, by the way … I think I'll just copy-and-paste it! :rolleyes:)

    Hint: [tex]\frac{(1+i)^n}{(1+i)^n-1}\,=\,1\,+\,\frac{1}{(1+i)^n-1}[/tex] :smile:
  4. May 5, 2008 #3


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    I would be inclined to simplify at first: let 1+ i= u. Then the equation is
    [tex]R= \frac{Piu^n}{u^n-1}[/tex]
    then rather than use tiny-tim's method (which is perfectly good) I would multiply on both sides by un- 1:
    [tex]Ru^n- R= Pi u^n[/tex]
    isolate the un term:
    [tex]Ru^n- Pi u^n= (R- Pi)u^n= R[/itex]
    [tex]u^n= \frac{R}{R- Pi}[/itex]
    to solve for n, you will now have to take a logarithm of both sides.

    (Don't forget to put 1+ i back in for u in the answer.)
  5. May 5, 2008 #4
    the logarithm

    So to isolate the n variable in [tex]u^n= \frac{R}{R- Pi}[/tex]

    would i have to take the logarithm base "u" on both sides? Or will any logarithm work?
  6. May 6, 2008 #5


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    Hi LordofDirT! :smile:

    Yes … n = (logR - log(R - pi))/logu, for any base of log. :smile:

    btw, the reason I suggested my way (instead of HallsofIvy's, which is fine) was to get (1+i)^n just once in the equation … I reckon I'm quite likely to make mistakes, and that lessens the possiblity slightly! :smile:
  7. Mar 30, 2009 #6
    Re: Annuity Equation "isolating i value" HELP!

    hi everybody!

    please help.... i need to solve the i value for this formula.....

    P = the principal = (63,000.00)
    R = the amortized payment = (2750.00)
    n = the Terms = (36 Months)

    P = R((1-(1/(1+i)power of n))/i)

    please i really need help to solve for i value....

  8. Mar 30, 2009 #7


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    Welcome to PF!

    Hi gardzrecah ! Welcome to PF! :smile:

    (btw, it's always better to start a new thread … more people will see it)

    (and try using the X2 tag just above the Reply box :wink:)

    Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
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