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Math Help - Macauley's duration formula, proof and dedution needed-Finance economics

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    Question Macauley's duration formula, proof and dedution needed-Finance economics

    I am searching for deduction step by step of Macauly's duartion formula, or its special form that looks like this:

    D= {(1+Y)/Y - [1+Y+T(c-Y)]/[(c(1+Y)^T-1))+Y]}
    where :
    D-duration
    Y-yield to maturity rate
    c-coupon rate
    T-elapsed time to yield to maturity

    I need this formula explained step by step and how do we get to this final form. I am sincearely grateful to any1 who can help me, but please, dont reply me with links, because i already scoped entire web and didnt find exact deduction and proof of this formula. So, i summon all Math genius to explain this formula to me. Thank You in advance
    Attached Thumbnails Attached Thumbnails Macauley's duration formula, proof and dedution needed-Finance economics-dsc00255.jpg  
    Last edited by matke90; October 29th 2012 at 02:34 PM. Reason: added upload picture of formula
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