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Thread: Transpose This Equation To Solve For i

  1. #1
    SGS
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    Transpose This Equation To Solve For i

    Can anyone transpose this equation to solve for i as a function of A, P, n ie, i = .....

    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 02:35 PM. Reason: Typo!!
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  2. #2
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    Re: Transpose This Equation To Solve For i

    Quote Originally Posted by SGS View Post
    Can anyone transpose this equation to solve for i as a function of A, P, n ie, i = .....
    A - P(((1 + i)n - 1)/( (1 - I) + (1 + i)n))
    There is no = sign posted. So no equation to solve.
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  3. #3
    MHF Contributor

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    Re: Transpose This Equation To Solve For i

    Now that you have the equal sign, your equation is
    A = P\frac{(1 + i)^n - 1}{(1 - i) + (1 + i)^n}

    The first, obvious step is to divide both sides by P:
    \frac{(1+ i)^n- 1}{(1- i)+ (1+ i)^n}= \frac{A}{P}

    Now multiply both sides by that denominator, (1- i)+ (1+ i)^n:
    (1+ i)^n- 1= \frac{A}{P}((1- i)+ (1+ i)^n).

    Now, rather than expand that "1+ i" to the nth power, I would let x= 1+ i. Then i= x- 1 so 1- i= 1- x+ 1= 2- x so that can be written as x^n- 1= \frac{A}{P}(x^n+ 2- x) and then
    \left(\frac{A}{P}- 1\right)x^n - x+ 3= 0.

    That is an nth degree polynomial equation for x. Unfortunately, there is no general method for solving nth degree polynomial equations.
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