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Math Help - Help required in a formula

  1. #1
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    Help required in a formula

    Hello all,

    x = [(a-b(1+i)^-n)*y] / [(1-(1+i)^(n-y))/i)+y].

    i need to get the reverse formulae for a,b,i,n and y. i need this information urgently. please help.

    Thanks in Advance

    Priyan
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tpriyan View Post
    Hello all,

    x = [(a-b(1+i)^-n)*y] / [(1-(1+i)^(n-y))/i)+y].

    i need to get the reverse formulae for a,b,i,n and y. i need this information urgently. please help.

    Thanks in Advance

    Priyan
    What, exactly, are you asking for? You need to solve the above equation for, say, y in terms of the remaining variables? (Then a, then b, then i, then n?)

    -Dan
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  3. #3
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    a and b are straightforward. <br /> <br />
a = x(\frac {1-(1+i)^{n-y}}{i}+y)+b(1+i)^{-n}
    <br />
b = (a - x(\frac{1-(1+i)^{n-y}}{i}+y))(1+i)^n

    It does not appear to be possible to solve explicitly for i and y. I have not proved this, but I cannot see any way to do it.

    n can be solved for by first forming a quadratic in (1+i)^n:
    <br />
x(\frac {1-(1+i)^{-y}(1+i)^n}{i}+y)-a+b(1+i)^{-n} = 0
    <br />
\frac {x}{i(1+i)^y}(1+i)^n+(\frac {x}{i}+xy-a)+b(1+i)^{-n} = 0
    <br />
(1+i)^n = \frac{a-xy-\frac{x}{i}\pm \sqrt{(\frac {x}{i} +xy-a)^2+4\frac {x}{i(1+i)^y}b}}{2\frac{x}{i(1+i)^y}}
    <br />
n = \frac {\log (\frac{a-xy-\frac{x}{i}\pm \sqrt{(\frac {x}{i} +xy-a)^2+4\frac {x}{i(1+i)^y}b}}{2\frac{x}{i(1+i)^y}})}{\log (1+i)}
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  4. #4
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    Quote Originally Posted by topsquark View Post
    What, exactly, are you asking for? You need to solve the above equation for, say, y in terms of the remaining variables? (Then a, then b, then i, then n?)

    -Dan
    Yes that is what i want
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