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Thread: Transpose An Equation

  1. #1
    SGS
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    Transpose An Equation

    Can anyone transpose this equation to solve for n as a function of A, P, i ie, n = .....
    A = P(((1 + i)n - 1)/( (1 - I) + (1 + i)n))

    Please show each step!



    Sorry for the typo! Added = sign after A
    Last edited by SGS; Aug 22nd 2017 at 01:36 PM. Reason: Typo
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  2. #2
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    Re: Transpose An Equation

    $A = P\dfrac{(1+i)^n-1}{(1-i)+(1+i)^n}$

    $\dfrac{A}{P} = \dfrac{(1-i)-(1-i)+(1+i)^n-1}{(1-i)+(1+i)^n} = 1+\dfrac{i-2}{(1-i)+(1+i)^n}$

    $\dfrac{A}{P}-1 = \dfrac{i-2}{(1-i)+(1+i)^n}$

    $\left(\dfrac{A}{P}-1\right) ((1-i)+(1+i)^n) = i-2$

    $\dfrac{A(1-i)}{P}-1+i+\left(\dfrac{A}{P}-1\right) (1+i)^n = i-2$

    $\left(\dfrac{A}{P}-1\right) (1+i)^n = \dfrac{A(i-1)}{P}-1$

    $(1+i)^n = \dfrac{\dfrac{A(i-1)}{P}-1}{\dfrac{A}{P}-1}$

    $n = \dfrac{ \ln \left( \dfrac{A(i-1)}{P} - 1\right) - \ln \left( \dfrac{A}{P} - 1 \right) }{\ln (1+i) }$
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  3. #3
    SGS
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    Re: Transpose An Equation

    Thank you for your answer!!

    I don't understand your nomenclature $, dfrac, left, right. Could you please explain or repost your answer in standard math nomenclature.

    Steve
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  4. #4
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    Re: Transpose An Equation

    Can you see post # 2? Or did you hit reply with quote and look at that?
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  5. #5
    SGS
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    Re: Transpose An Equation

    Both Post #2 and Reply With Quote have $, dfrac, left, right.
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  6. #6
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    Re: Transpose An Equation

    Quote Originally Posted by SGS View Post
    Both Post #2 and Reply With Quote have $, dfrac, left, right.
    Those commands have nothing to do with mathematics.

    They are type-settings to make the symbols.
    1)n = \dfrac{ \ln \left( \dfrac{A(i-1)}{P} - 1\right) - \ln \left( \dfrac{A}{P} - 1 \right) }{\ln (1+i) } is the code required to see
    2)$n = \dfrac{ \ln \left( \dfrac{A(i-1)}{P} - 1\right) - \ln \left( \dfrac{A}{P} - 1 \right) }{\ln (1+i) }$

    Line #1) is exactly the same as line #2) except 2) begin with and ends with $. That tell the browser to display LaTex.

    SEE HERE
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  7. #7
    SGS
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    Re: Transpose An Equation

    Thank you 1111
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  8. #8
    SGS
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    Re: Transpose An Equation

    Now how do I copy and paste the answer in Post #2 into Word and see only standard mathematical notation?
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  9. #9
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    Re: Transpose An Equation

    Quote Originally Posted by SGS View Post
    Can anyone transpose this equation to solve for n as a function of A, P, i ie, n = .....
    A = P(((1 + i)n - 1)/( (1 - I) + (1 + i)n))
    Please show each step!
    Curious: that's obviously a financial formula;
    WHAT does it do?
    With p=100, i=.01 and n=12, result is a = 5.99128....
    WHAT d'heck is that?

    Also, you're showing i and I : are they the same?
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  10. #10
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    Re: Transpose An Equation

    OK; assuming i and I are SAME, this will work:

    n = LOG[(a(1 - i) + p) / (p - a)] / LOG[1 + i]
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  11. #11
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    Re: Transpose An Equation

    Quote Originally Posted by DenisB View Post
    OK; assuming i and I are SAME, this will work:

    n = LOG[(a(1 - i) + p) / (p - a)] / LOG[1 + i]
    I is the identity matrix, you fool! Just kidding
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  12. #12
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    Re: Transpose An Equation

    Quote Originally Posted by abender View Post
    I is the identity matrix, you fool! Just kidding
    You on A BENDER?!!!!
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  13. #13
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    Re: Transpose An Equation

    Simpler still:

    u = 1 + i
    v = 1 - i

    n = LOG[(p + av)/(p - a)] / LOG[u]
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  14. #14
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    Re: Transpose An Equation

    Quote Originally Posted by SGS View Post
    Now how do I copy and paste the answer in Post #2 into Word and see only standard mathematical notation?
    You probably can't. As far as I have been able to figure out, Word does not support LaTeX but has its own (not very good in my opinion) mathematical option.

    Do you see a summation symbol when you look below?

    $\displaystyle \sum_{j=1}^nx^j$

    If so, then your browser is rendering LaTeX properly.

    If instead you see \displaystyle \sum_{j=1}^nx^j, your browser is not rendering LaTeX properly.
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