Financial Maths, STD1 F3 2025 HSC 24 v1

A used car has a sale price of $\$18\,600$. In addition to the sale price, the following costs are charged:

transfer of registration $50
stamp duty which is calculated at $3 for every $100, or part thereof, of the sale price.

Tahlia borrows the total amount to be paid for the car, including transfer of registration and stamp duty. Simple interest at the rate of 7.2% per annum is charged on the loan. The loan is to be repaid in equal monthly repayments over 4 years.

Calculate Tahlia's monthly repayment, correct to the nearest cent. (5 marks)

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$\$515.41$

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$\text{Stamp duty}=\dfrac{18\,600}{100}\times 3=\$558$

$\text{Total borrowed}=18\,600+50+558=\$19\,208$

$\text{Interest}=Prn=19\,208\times 0.072\times 4=\$5531.904$

$\text{Total to repay}=19\,208+5531.904=\$24\,739.904$

$\therefore\ \text{Monthly repayment}=\dfrac{24\,739.904}{48}=515.4146…\approx \$515.41$