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 oravikiran June 13th, 2012 04:33 AM

please solve this simple equation, thx

The equation is

1000 = 272/ (1+i)^0.25 + 272/(1+i)^0.5 + 544/(1+ i)^1

find the value of i.

The result is i = 0,13185

why wondering how the result came. can you please let me know the each step taken for calcuation.

Thanks , kiran

 MarkFL June 13th, 2012 09:04 AM

Re: please solve this simple equation, thx

We are given:

$1000=\frac{272}{(1+i)^{\small{\frac{1}{4}}}}+\frac {272}{(1+i)^{\small{\frac{1}{2}}}}+\frac{544}{1+i}$

Multiply through by $\frac{1+i}{8}$ and rearrange to obtain:

$125(1+i)-34(1+i)^{\small{\frac{3}{4}}}-34(1+i)^{\small{\frac{1}{2}}}-68=0$

Let $u^4=1+i$:

$125u^4-34u^3-34u^2-68=0$

Use a numerical method to determine one of the real roots is:

$u\approx1.0314488454215854323$

$1+i=u^4\approx1.1318549545275935$

$i\approx0.1318549545275935$

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