Mathematics Standard • Year 12 • Module 7 • Lesson 9
Credit Cards — Past-Paper Style
Practise HSC Mathematics Standard 2-style writing on credit-card maths — three short-answer questions and one longer scenario with marking criteria.
1. Short-answer questions
1.1 A credit card has a balance of $4,500 at 19.99% p.a. compounded daily.
(a) Calculate the daily interest charged on this balance.
(b) Calculate the monthly interest (using monthly r = 0.1999/12). 2 marks Band 3
1.2 A credit card is advertised at 21.99% p.a. compounded daily.
(a) Calculate the effective annual rate to 2 dp.
(b) Explain in one sentence why the effective rate exceeds the advertised 21.99%. 3 marks Band 3-4
1.3 A balance transfer offers 0% for 15 months on $6,000 of existing debt, with a 1.5% transfer fee. The card holder can afford $400/month.
(a) Calculate the transfer fee and the new opening balance.
(b) State whether the new balance will be cleared within the 15-month promotional period.
(c) The same $400/month paid on the existing 20% card would total $6,000 of payments but leave roughly $300 of unpaid interest still owed. State the dollar saving from accepting the transfer. 4 marks Band 4
2. Extended response
2.1 Hannah has a $3,000 credit-card balance at 19.99% p.a. (use monthly r = 0.1999/12 ≈ 0.01666). She is choosing between three repayment strategies, with no further purchases on the card.
Strategy A: Pay only the $60 monthly minimum. Projected to take approximately 9.25 years (111 months), total paid ≈ $6,660.
Strategy B: Pay $150 monthly. Projected to clear in ≈ 24 months, total paid ≈ $3,600.
Strategy C: Transfer to a 0% card for 12 months with a 2% transfer fee, then pay $260/month and clear within the 12-month promotional window.
(a) Calculate the total interest under Strategy A.
(b) Calculate the total interest under Strategy B.
(c) Calculate the transfer fee under Strategy C and the total amount Hannah will pay across the 12 months.
(d) Recommend the best strategy for Hannah, naming the strategy and the dollar interest saved compared to Strategy A, and explain in one sentence why minimum payments are so costly. 7 marks Band 5-6
Explicit marking criteria
Part (a) — 1 mark
• 1 mark — correct total interest for Strategy A = total paid − PV.
Part (b) — 1 mark
• 1 mark — correct total interest for Strategy B.
Part (c) — 2 marks
• 1 mark — correct transfer fee = 0.02 × $3,000.
• 1 mark — correct total paid under Strategy C.
Part (d) — 3 marks
• 1 mark — comparison of all three totals on the same "total dollar cost" basis.
• 1 mark — recommendation names the chosen strategy AND quotes the dollar saving vs Strategy A.
• 1 mark — explanation links minimum payments to compounding interest on a barely-reducing balance.
Your response:
Stuck on (d)? After computing the three total costs, the best strategy is simply the cheapest — but the conclusion must name it, state the dollar gap vs Strategy A, and explain why minimums fail.How did this worksheet feel?
What I'll revisit before next class:
1.1 — Daily and monthly interest on $4,500 (2 marks)
Sample response. (a) I_day = 4,500 × 0.1999 / 365 ≈ $2.46/day. (b) I_month = 4,500 × 0.1999 / 12 ≈ $74.96.
Marking notes. 1 mark — correct daily interest (must divide by 365, not 12). 1 mark — correct monthly interest. Using r = 0.1999 / 30 for "daily" scores 0/1 for that part.
1.2 — Effective annual rate (3 marks)
(a) Sample response. r_eff = (1 + 0.2199/365)³⁶⁵ − 1 ≈ 0.2459 = 24.59% p.a.
(b) Sample response. Each day's interest is added to the balance, so the next day's interest is charged on a slightly larger amount; over 365 days this daily compounding lifts the realised rate above the nominal 21.99%.
Marking notes. (a) 1 mark — correct formula. 1 mark — correct answer to 2 dp. (b) 1 mark — explanation references "interest on interest" or compounding.
1.3 — Balance transfer (4 marks)
(a) Sample response. Fee = 6,000 × 0.015 = $90. New balance = $6,090.
(b) Sample response. 6,090 / 400 = 15.225 months → just barely not cleared within 15 months; she would need $406/month to clear in exactly 15 months.
(c) Sample response. Existing card: $6,000 paid + ~$300 unpaid interest = $6,300 effective cost. Transfer card: $6,090 cleared. Saving ≈ $210.
Marking notes. (a) 1 mark — fee and new balance. (b) 1 mark — correct conclusion with calculation. (c) 1 mark — comparison setup. 1 mark — correct dollar saving.
2.1 — Hannah's three strategies (7 marks): sample Band-6 response with annotations
Sample Band-6 response.
(a) Strategy A — minimum payments.
Total interest = 6,660 − 3,000 = $3,660. [1 mark — correct total interest = total paid − PV.]
(b) Strategy B — $150/month.
Total interest = 3,600 − 3,000 = $600. [1 mark — correct total interest.]
(c) Strategy C — balance transfer.
Transfer fee = 3,000 × 0.02 = $60. [1 mark — correct fee.]
New balance = $3,060. Monthly $260 × 12 = $3,120 total paid. [1 mark — correct total = monthly × 12.]
(d) Comparison and recommendation.
Total dollar cost: A = $6,660, B = $3,600, C = $3,120. Strategy C is cheapest. [1 mark — comparison of all three on the same total-cost basis.]
Conclusion: Hannah should take Strategy C — by transferring the balance and paying $260/month for 12 months, she pays $6,660 − $3,120 = $3,540 less than if she only paid the minimum (Strategy A). [1 mark — names Strategy C and quotes the dollar saving vs Strategy A.] Minimum payments are so costly because most of each $60 is consumed by the monthly interest charge — only about $10 of every payment actually reduces the principal, so interest keeps compounding on a balance that barely shrinks. [1 mark — explanation links minimum payments to compounding on barely-reducing balance.]
Total: 7/7.
Band descriptors for marker.
Band 3: Strategy A interest correct, Strategy B interest correct, Strategy C transfer fee omitted or total computed without the fee. ≈ 2-3 marks.
Band 4: All three numerical parts correct but no comparison sentence or no dollar saving stated. ≈ 4-5 marks.
Band 5: Full numerical solution + recommendation naming Strategy C with dollar saving, but no explanation of why minimum payments fail. ≈ 6 marks.
Band 6: Complete: three totals correct, recommendation with dollar saving vs Strategy A, AND a clear explanation of the minimum-payment trap. 7/7.