Resources for Investing Money With Regular Installments
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Questions
8
With Worked SolutionClick Here -
Video Tutorials
1
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Investing Money With Regular Installments Theory
![For these questions you will need to know the sum to \(n\) terms of a G.P. \\ \(\text { i.e. } \quad S_n=\dfrac{a\left(r^n-1\right)}{r-1} \)\\ \textbf{Example}\\ How much superannuation will there be at the end of 25 years if \(\$ 810\) is invested at \(8 \%\) pa. at the beginning of each year?\\ \textbf{Solution}\\ $\begin{aligned} & \text { The first amount } A_1=810(1.08)^{25} \\ & \text { The second amount } A_2=810(1.08)^{24} \\ & \text { The final amount } A_{25}=810(1.08)^{\prime} \\ & \text { The total amount }=810(1.08)^1+810(1.08)^2+\cdots+810(1.08)^{25} \\ & \qquad\qquad\qquad\qquad =810\left[1.08+1.08^2+\cdots 1.08^{25}\right] \\ & \text { Sum of the GP }=\frac{1.08\left(1.08^{25}-1\right)}{0.08} \\ & \qquad\qquad\qquad\quad=78.9544 \ldots \\ & \therefore \text { Total }=810 \times 78.9544 . . \\ &\qquad\qquad =\$ 63953.08 \end{aligned}$\\](/media/hynpj0eh/4805.png)