Financial Maths, STD2 EO-Bank 34

Farah wants to buy a commercial espresso machine for her cafe at a cost of $4200. She has decided to pay off whatever she owes in a single amount 75 days after the purchase, and is weighing up two ways to fund it.

A credit card that compounds interest daily at 17% per annum, but does not charge interest during the first 25 days after a purchase.
A personal loan on which simple interest is charged at 8.9% per annum.

Advise Farah on the cheaper option, backing up your recommendation with the relevant calculations. (4 marks)

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$\text{Credit card interest}=\$98.93$

$\text{Personal loan interest}=\$76.81$

$\text{As }\$76.81\lt\$98.93,\text{ Farah should choose the personal loan.}$

Show Worked Solution

$\text{Days accruing interest}=75-25=50$

$\text{Credit card option (interest compounds daily):}$

$\text{Amount owing}$	$=4200\left(1+\dfrac{0.17}{365}\right)^{50}$
	$=4298.931\ldots$
	$=\$4298.93\ \text{(nearest cent)}$

$\therefore\ \text{Interest}=4298.93-4200=\$98.93$

$\text{Personal loan option (simple interest applies):}$

$I=Prn$	$=4200\times 0.089\times\dfrac{75}{365}$
	$=76.808\ldots$
	$=\$76.81\ \text{(nearest cent)}$

$\therefore\ \text{As }\$76.81\lt\$98.93,\text{ the personal loan}$

$\text{is cheaper, so Farah should choose it.}$

\(\text{Amount owing}\)	\(=4200\left(1+\dfrac{0.17}{365}\right)^{50}\)
	\(=4298.931\ldots\)
	\(=\$4298.93\ \text{(nearest cent)}\)

\(I=Prn\)	\(=4200\times 0.089\times\dfrac{75}{365}\)
	\(=76.808\ldots\)
	\(=\$76.81\ \text{(nearest cent)}\)