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I have this equation:

960 - 84.60 * ((1-(1+i)^-12)/i) == 0

I simplify ( 1+i)^-12 with a Taylor series ( 1 + x)^a.

but I obtain i == 0.087201167 but the real result should be i == 0.00753 (approximately).

P.S.: My solution

( 1 + i)^-12 == 1 - 12i + 78i^2 + 364i^3

Then:

1 -(1+i)^-12 == 12i - 78i^2 + 364i^3

Then I collect i and I simplify so I obtain:

960 - 84.60 * (12 - 78 i + 364 i^2) == 0

And I obtain:

-55.20 + 6598.80 i - 30794.40i^2 == 0

I apply the Quadratic Formula and I obtain:

i == 0.087201167 and i = 2.055

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migrated from mathematica.stackexchange.com Sep 19 '13 at 3:26

This question came from our site for users of Mathematica.

1  
I don't see an equation. Could you please provide the code you tried? –  Sjoerd C. de Vries Sep 18 '13 at 17:40
    
Stefano, is this a question about how to use the Mathematica software or a question about how to deal with the equation (i.e. math)? –  Szabolcs Sep 18 '13 at 17:43
    
You lost a factor of 'i' in your "collect and simplify" step. [What this has to do with Mathematica is that, had you used it throughout, this would have been an unlikely occurence.] –  Daniel Lichtblau Sep 18 '13 at 18:02
    
@DanielLichtblau You can check these steps are correct until the last line, the result should be i == 0.00872 || i == 0.205566 it is different by a factor 10. Nevertheless approximate solution i == 0.00872 is correct, it just shouldn't be i == 0.00753. –  Artes Sep 18 '13 at 18:26
1  
But How you have found i = 0.00872 and i = 0.205566 –  Stefano Sep 18 '13 at 18:29

2 Answers 2

Solve[960 - 84.60*((1 - (1 + i)^-12)/i) == 0, i, Reals]

{{i -> -1.77547}, {i -> 0.00870777}}

Plot[960 - 84.60*((1 - (1 + i)^-12)/i), {i, -2, .1}, 
     PlotRange -> {-.01, 0.01}, Axes -> {True, False}]

Mathematica graphics

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Thank you very much for your answer but I need the Formula in order to add it to Excel. But I don't obtain 0.0087 that is OK! –  Stefano Sep 18 '13 at 17:54

Equation

$$ 960 - 84.6 \frac{ 1 - (1+i)^{-12}}{i} = 0$$

Taylor expansion

$$ (1+i)^{-12} \approx -364 i^3+78 i^2-12 i+1 $$

Approximate Equation

$$ 960 - 84.6 \frac{ 364 i^3-78 i^2+12 i }{i} = 0$$

With solutions

$$ i = 0.00872 \;,\;\; i = 0.205566 $$

So what is your question here?

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