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Math Help - Annuity problem - starter

  1. #1
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    Annuity problem - starter

    Can someone give me a starting hint with this one, ie. how to set up the equation of value? I'm not asking for you to do the question, just point me in the right direction with setting it up because ive tried it 6 times and i am obviously missing something. This is the entire question:


    George plans to deposit $1200 at the end of every six months for fifteen years, so that hwe can withdraw equal amounts at the end of every six months for twenty years. If interest is j2 = 14.5%, how much will George be able to collect every six months?


    I tried setting it up like the following, which didnt work:


    1200[(1 + 0.0725)^30 - 1 / (0.0725)] [ 1 + 0.0725 ^-10 ] = R [ 1- (1 + 0.0725 ^-40 / 0.0725 ]
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  2. #2
    MHF Contributor
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    1) Be much, MUCH more careful with your notation.

    These are VERY different...

    [(1 + 0.0725)^30 - 1 / (0.0725)]
    [[(1 + 0.0725)^30 - 1 ]/ (0.0725)]

    These are VERY different...

    1 + 0.0725 ^-10
    (1 + 0.0725) ^(-10)

    2) What is that middle factor? [ 1 + 0.0725 ^-10 ]

    3) Simplify your life with definitions.

    i = 0.0725
    v = 1/(1.0725) = 1/(1+i)
    r = 1/v = 1+i

    This gives:

    (1-r^30)/(1-r) = R[(1-v^40)/(i)]

    WAY simpler!
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