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NSW Y12 Maths - Advanced Series and Finance Simple and Compound Interest

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Simple and Compound Interest Theory

The formula for simple interest is \(I=P r n\) where \(I\) is the interest \(r\) is the rate per period of time and \(n\) is the number of periods.\\ The formula for compound interest is \(A=P(1+r)^n\) where \(A\) is the total amount hence \(I=A-P\).\\ \begin{multicols}{2} \textbf{Example 1} \\ %15901 Find the simple interest rate if \$10,000 earns an interest of \$2,000 over a period of 5 years. \\ \textbf{Example 1 solution}\\ $\begin{aligned} I=\operatorname{Prn} \rightarrow 2000 &=10000 \times r \times 5 \\ 2000 &=50000 \times r\\ r &=\frac{2000}{50000} \\ &=0.04 \\ \therefore r &=4\%\ \text{p. a} \end{aligned}$\\ \columnbreak \textbf{Example 2}\\ %15902 Find the compound interest rate if \$10,000 earns an interest of \$2,000 over a period of 5 years.\\ \textbf{Example 2 solution}\\ $\begin{aligned} A=P(1+r)^{n} \rightarrow 12000=10000(1+r)^{5} & \\ \frac{12000}{10000}=(1+r)^{5} \rightarrow 1+r &=(1.2)^{\frac{1}{5}} \\ r &=0.037 \\ r &=3.7\%\ \mathrm{p} \cdot \mathrm{a} \end{aligned}$ \end{multicols}

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  • Simple and Compound Interest - Video - Compound interest Appreciation

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