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NSWMaths Standard 2Quick questions

Year 12: Financial Mathematics

Quick questions on Credit card interest, daily compounding and the cost of revolving debt for HSC Maths Standard 2

12short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is how credit card interest works?
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A credit card charges a high annual interest rate (typically 1313-22%22\% in Australia, per RBA statistics) compounded daily on any balance carried beyond the due date.
What is daily rate?
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$rday=R365.r_{\text{day}} = \frac{R}{365}.$
What is balance after nn days?
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Using compound interest with daily compounding:
What is effective annual rate?
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A daily-compounded rate has a slightly higher effective annual rate than the nominal rate:
What is minimum monthly repayment?
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Cards usually require a minimum monthly repayment of 22-3%3\% of the closing balance (or a fixed minimum, whichever is greater). Paying only the minimum means the balance reduces extremely slowly while interest keeps compounding, so the debt can persist for decades.
What is statement period?
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A typical statement period is one month. Interest is calculated daily and added to the balance at the end of the statement period.
What is carrying a balance (Australian context, 2025)?
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A cardholder has a balance of \3500at at 18.99\%perannumdailycompounding.Theymakenopurchasesandnorepaymentsfor per annum daily compounding. They make no purchases and no repayments for 30$ days.
What is minimum repayment trap?
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A \5000balanceat balance at 19\%perannumwitha per annum with a 2\%$ minimum monthly payment. If no further purchases are made and only the minimum is paid:
What is forgetting the back-dating rule?
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If the balance is not paid in full by the due date, interest typically applies from the original purchase date on the entire balance, including the part already paid.
What is wrong number of days?
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Count actual calendar days, not weeks or months. February has 2828 days, not 3030.
What is annual rate substituted directly?
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Use the daily rate R/365R/365 for daily compounding, then raise to the number of days.
What is misreading minimum payment?
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2%2\% of the balance is usually well below the monthly interest charge. Paying the minimum barely reduces the balance. :::

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