Financial Maths, STD2 2025 HSC 27 (Adapted)

Noor buys a lounge suite for $650 on 3 April using a credit card. The card has an interest-free period of 30 days from and including the date of purchase. Interest is charged on purchases, compounding daily at a rate of 16.8% per annum, from and including the day following the interest-free period.

No other purchases were made on this credit card.

The account was paid in full on 20 May.

What was the total interest charged when the account was paid in full? (3 marks)

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$\text{Interest charged}=\$5.41$

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$\text{Total days (3 April to 20 May)}=28+20=48$

$\text{Interest-free days}=30$

$\text{Days accruing interest}\ (n)=48-30=18$

$\text{Daily interest rate}\ (r)=\dfrac{0.168}{365}=0.00046027\ldots$

$\text{Amount owing}=650(1+0.00046027\ldots)^{18}=\$655.41$

$\therefore\ \text{Interest charged}=655.41-650=\$5.41$