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Math Help - Tricky Superannuation Problem

  1. #1
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    Tricky Superannuation Problem

    You are 44 years old, you wish to retire at 65.

    You earn $75,000 a year and already have $100,000 in your super account.

    You have an average annual super rate of 5.1%.

    Calculate by formula the future value of your superannuation if your contributions continue to be 9% of your income but your income increases on average by 3% per annum.

    The only formula given is,

    Sn = a[(1+r)^n -1] r



    Where a = repayment, (monthly, fortnightly etc)
    r = growth rate, eg
    nominal interest rate per annum number of interest periods per year

    and n =
    time in years * number of interest periods per year



    dont even know if thats the right formula to be using, i think a new formula needs to be developed im not sure



    thanks for the help anyway guys
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  2. #2
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    Quote Originally Posted by I Drink and Derive View Post
    You are 44 years old, you wish to retire at 65.
    You earn $75,000 a year and already have $100,000 in your super account.
    You have an average annual super rate of 5.1%.
    Calculate by formula the future value of your superannuation if your contributions continue to be 9% of your income but your income increases on average by 3% per annum.
    The only formula given is,
    Sn = a[(1+r)^n -1] r
    75000 * .09 = 6750 ; these are contributions without the 3% increase

    That formula gives you the future value of annual deposits:
    FV = 6750[(1 + .051)^(65-44) - 1] / .051

    You also need the future value of the 100,000; 100000(1 + .051)^21

    Are you able to follow that? What is the result of each?
    Last edited by Wilmer; August 12th 2009 at 09:59 AM. Reason: none
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  3. #3
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    try this out

    <br />
100,000\left( {1.051} \right)^{21}  + 75,000\left( {0.09} \right)\left( {1.03} \right)\frac{{\left( {1.051} \right)^{21}  - \left( {1.03} \right)^{21} }}{{0.051 - 0.03}}<br />
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  4. #4
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    Jonah, in this portion: 75,000(0.09)(1.03)
    I don't think the 1.03 is required.
    But works fine otherwise.
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  5. #5
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    Quote Originally Posted by Wilmer View Post
    Jonah, in this portion: 75,000(0.09)(1.03)
    I don't think the 1.03 is required.
    But works fine otherwise.
    typing is torture due to keyboard error
    3 possibilities

    possibility 1: 1st contrribution is included in $100,000

    <br />
\left\{ {\left[ {100,000 - 75,000\left( {0.09} \right)} \right] + 75,000\left( {0.09} \right)} \right\}\left( {1.051} \right)^{21}  + <br />
<br />
75,000\left( {0.09} \right)\left( {1.03} \right)\frac{{\left( {1.051} \right)^{21}  - \left( {1.03} \right)^{21} }}{{0.051 - 0.03}}<br />
    <br />
 \Leftrightarrow 100,000\left( {1.051} \right)^{21}  + 75,000\left( {0.09} \right)\left( {1.03} \right)\frac{{\left( {1.051} \right)^{21}  - \left( {1.03} \right)^{21} }}{{0.051 - 0.03}}<br />

    possibility 2: 1st contrribution is not included in $100,000

    <br />
\left[ {100,000 + 75,000\left( {0.09} \right)} \right]\left( {1.051} \right)^{21}  + 75,000\left( {0.09} \right)\left( {1.03} \right)\frac{{\left( {1.051} \right)^{21}  - \left( {1.03} \right)^{21} }}{{0.051 - 0.03}}<br />

    possibility 3: 1st contribution is on 45th birthday

    <br />
100,000\left( {1.051} \right)^{21}  + 75,000\left( {0.09} \right)\frac{{\left( {1.051} \right)^{21}  - \left( {1.03} \right)^{21} }}{{0.051 - 0.03}}<br />
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  6. #6
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    Roger!
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