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Math Help - Superannuation Geometric Series Question

  1. #1
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    Superannuation Geometric Series Question

    Qu:
    An amount of $3000 is invested in a superannuation fund at the start of each year for 18 years. The interest at a rate of 9% p.a. is paid half-year.

    How much is the investment worth after 18 years?

    ---------------------

    I don't understand how you need to adjust the equation for the 9% interest being paid every half a year...
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  2. #2
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    Last edited by mr fantastic; November 25th 2010 at 11:48 AM.
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  3. #3
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    Quote Originally Posted by rusdev View Post
    Qu:
    An amount of $3000 is invested in a superannuation fund at the start of each year for 18 years. The interest at a rate of 9% p.a. is paid half-year.

    How much is the investment worth after 18 years?

    ---------------------

    I don't understand how you need to adjust the equation for the 9% interest being paid every half a year...
    You are trying to find future value of an annuity due. The plain formula for this is
    FVAD = R x FVIFAD(i%,n)
    or
    FVAD = R x (1+i) [(1+i)^n - 1]/i

    But since we have semiannual compounding we divide i by 2 and multiply n by 2

    FVAD = R x (1+i/2) [(1+i/2)^2n - 1]/(i/2)
    FVAD = 3000 x (1+9%/2) [(1+9%/2)^36 - 1]/(9%/2)
    FVAD = 3000 x (1+4.5%) [(1+4.5%)^36 - 1]/(4.5%)
    FVAD = 3000 x (1.045) [(1.045)^36 - 1]/(0.045)
    FVAD = 3000 x (1.045) [(1.045)^36 - 1]/(0.045)
    FVAD = 3000 x (1.045) [4.8773784614756470522995531708692-1]/0.045
    FVAD = 3000 x (1.045) [3.8773784614756470522995531708692]/0.045
    FVAD = 3000 x (1.045) [3.8773784614756470522995531708692]/0.045
    FVAD = 3000 x (1.045) 86.163965810569934495545626019316
    FVAD = 3000 x 90.041344272045581547845179190185
    FVAD = $270,124

    To see how I got the 90.04 for FVIFAD try this online calculator FVIFAD > Download FVIFAD Table > Online FVIFAD Calculator where you enter 4.5% for interest rate and 36 for periods

    To see how to get the FVAD value of $270,124, try this online calculator Online Calculator for Future Value of an annuity due where you enter 3000 for amount and the interest rate as 4.5% and 36 for period
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