Financial Maths, STD2 2019 HSC 27 (Adapted)

Bianca has a credit card that offers no interest-free period. At the end of each month, interest is added to the account at 19.5% per annum, compounded daily. Interest is worked out from the day a purchase is made (included) through to the last day of the month (included).

Part of Bianca’s June statement is shown below, with two figures left blank.

For this account, the minimum payment is set at 3% of the closing balance on 30 June.

Find the minimum payment, giving your answer to the nearest cent. (3 marks)

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$\text{Minimum payment}=\$78.42$

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$\text{Days of interest}\ (n)=\ \text{21 June – 30 June}=10$

$\text{Daily interest rate}\ (r)=\dfrac{0.195}{365}=0.0005342\ldots$

$\text{Closing balance}=2600(1+0.0005342\ldots)^{10}=\$2613.92$

$\text{Minimum payment}$	$=\dfrac{3}{100}\times 2613.92$
	$=78.4176\ldots$
	$=\$78.42\ \text{(nearest cent)}$

\(\text{Minimum payment}\)	\(=\dfrac{3}{100}\times 2613.92\)
	\(=78.4176\ldots\)
	\(=\$78.42\ \text{(nearest cent)}\)