Resources for Loan Repayments
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Questions
11
With Worked SolutionClick Here -
Video Tutorials
1
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HSC Questions
6
With Worked SolutionClick Here
Loan Repayments 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}\\ Tony borrows \$10000 from the bank and pays back the loan in monthly payments over 5 years. If the loan incurs interest at \(12 \% p . a\), find the amount of each payment.\\ \textbf{Solution}\\ $\begin{aligned} \text { For the first month } \quad A_1&=10000(1.01)^1-M . \\ \text { For the second month } \quad A_2&=\left[10000(1.01)^1-M\right] 1.01-M \\ &=10000(1.01)^2-M(1+1.01) \\ \text { For the 60th month } \quad A_{60}&=10000(1.01)^{60}-M(1+1.01+\cdots+ 1.01^{59}) \\ \text { Summing the G.P } \quad S_{60}&=\frac{1\left(1.01^{60}-1\right)}{0.01} \\ & =81.6697 \\ \text { When the loan is repaid } A_{60}&=0 \\ \therefore 0&=10000(1.01)^{60}-81.6697 M \\ M&=10000(1.01)^{60} \div 81.6697 \\ &=\$ 222.44 . \end{aligned}$\\](/media/rwgdmb1n/4806.png)