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Thread: Superannuation

  1. #1
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    Superannuation

    $3000 is invest yearly at 9%pa which is paid each half year, for 18yrs. Find the amount of the investment after 18yrs
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  2. #2
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    $\displaystyle A = P \left(1+\frac{r}{100}\right)^n$

    where $\displaystyle P= 3000, r = 9$ & $\displaystyle n = 18$

    $\displaystyle A = 3000 \left(1+\frac{9}{100}\right)^{18}= \dots$
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  3. #3
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    Hello, nerdzor!

    $3000 is invested yearly at 9% pa which is paid each half-year.
    Find amount of the investment after 18 years.
    This is an annuity.

    Formula: .$\displaystyle A \:=\:D\!\cdot\!\frac{(1+i)^n-1}{i}$

    . . where: .$\displaystyle \begin{Bmatrix}D &=& \text{periodic deposit} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \\ A &=& \text{final amount} \end{Bmatrix}$


    We have: .$\displaystyle D \:=\:3000 \qquad i \:=\:\frac{9\%}{2} \:=\:0.045 \qquad n \:=\: 36 $
    Hence: .$\displaystyle A \;=\;3000\!\cdot\!\frac{1.045^{36}-1}{0.045} \;=\;258491.8974 $

    The investment will be worth $\displaystyle \$258,\!491.90$

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