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Depreciation, credit cards and reducing balance loans: HSC Maths Standard 1 Year 12

Syllabus dot point

“Calculate the depreciation of an asset using the straight-line and declining-balance methods, calculate interest, closing balance and minimum payment on a credit card statement, and investigate reducing balance loans using tables, spreadsheets and online calculators”

HSCMaths Standard 1Year 12: Financial Mathematics9 min read

Quick answer

Straight-line depreciation subtracts the same amount each period (S=V0−DnS = V_0 - Dn); declining-balance depreciation subtracts the same percentage (S=V0(1−r)nS = V_0(1 - r)^n). Credit cards charge interest on unpaid balances and cash advances, so paying only the minimum is costly. In reducing balance loans, interest is charged on the balance owing each period, then the repayment is subtracted.

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  1. What this dot point is asking
  2. The answer
  3. Practice questions

What this dot point is asking

You need to understand how assets lose value (depreciation), how credit cards charge interest, and how reducing balance loans are repaid. NESA's topic guide emphasises using real credit card statements, spreadsheets and online loan calculators, and understanding that the compound interest formula gives depreciation when the rate is negative.

The answer

Depreciation

  • Straight-line depreciation: the value falls by the same amount each period (linear).

S=V0−DnS = V_0 - Dn

  • Declining-balance depreciation: the value falls by the same percentage each period (exponential decay). It is the compound interest formula with a negative rate:

S=V0(1−r)nS = V_0(1 - r)^n

SS is the salvage value, V0V_0 the initial value. Declining-balance depreciation falls fastest in the early years.

Credit cards

A credit card statement shows the opening balance, purchases, cash advances, payments, interest, closing balance, minimum payment and due date.

Credit card essentials
  • Interest-free period: no interest on purchases if the full closing balance is paid by the due date.
  • Interest is often calculated daily (annual rate ÷ 365) on the balance owing, from the purchase date if the balance is not paid in full.
  • Cash advances usually attract interest from the day they are taken, often at a higher rate.
  • Minimum payment: often a percentage of the closing balance or a set minimum; paying only this keeps you in debt for a long time.

Reducing balance loans

Each period: interest is added on the balance owing, then the repayment is subtracted.

closing balance=opening balance+interest−repayment\text{closing balance} = \text{opening balance} + \text{interest} - \text{repayment}

Loan tables, spreadsheets and online calculators show how changing the amount borrowed, interest rate or repayment affects the time to repay and the total interest.

Worked example

A credit card has an opening balance of $0, a purchase of $800 on 1 June, and interest of 19.8% p.a. charged daily from the purchase date because the balance is not paid in full. Find the interest for 30 days.

  1. Daily rate =0.198365=0.000542466= \frac{0.198}{365} = 0.000542466.
  2. Simple daily interest for 30 days: 800×0.000542466×30=$13.02800 \times 0.000542466 \times 30 = \$13.02.
  3. Closing balance =800+13.02=$813.02= 800 + 13.02 = \$813.02.
Common traps

Using 1+r1 + r for depreciation. Declining balance uses 1−r1 - r.

Forgetting to add interest before subtracting the repayment in a loan table.

Assuming the interest-free period applies to cash advances.

Practice questions

Original practice questions graded from foundation to exam level, each with a full worked solution. Try them before revealing the solution.

foundation3 marks
A laptop bought for 1800 dollars depreciates by 300 dollars per year (straight-line). Find its value after 4 years, and after how many years it is worth nothing.
Show worked solution →

S=1800−300×4=$600S = 1800 - 300 \times 4 = \$600.

Worth nothing when 1800−300n=01800 - 300n = 0, so n=6n = 6 years.

Marking guide: 1 mark for substitution, 1 mark for $600, 1 mark for 6 years.

core4 marks
A 32 000 dollar ute depreciates at 18% p.a. using the declining-balance method. Find its value after 3 years and the total depreciation.
Show worked solution →

S=32 000(1−0.18)3=32 000×0.823=32 000×0.551368=$17 643.78S = 32\,000(1 - 0.18)^3 = 32\,000 \times 0.82^3 = 32\,000 \times 0.551368 = \$17\,643.78.

Total depreciation =32 000−17 643.78=$14 356.22= 32\,000 - 17\,643.78 = \$14\,356.22.

Marking guide: 1 mark for the formula with 1−r1 - r, 1 mark for 0.82 cubed, 1 mark for the value, 1 mark for total depreciation.

exam6 marks
A 10 000 dollar personal loan charges 12% p.a. interest, calculated monthly on the balance owing, with repayments of 350 dollars per month. Complete the first two rows of the loan table (month, opening balance, interest, repayment, closing balance) and explain why the balance falls faster over time.
Show worked solution →

Monthly rate =0.1212=0.01= \frac{0.12}{12} = 0.01.

Month Opening balance Interest (1%) Repayment Closing balance
1 $10 000.00 $100.00 $350 $9750.00
2 $9750.00 $97.50 $350 $9497.50

Each month, interest is charged only on the balance owing. As the balance falls, the interest falls, so more of each $350 repayment goes towards reducing the principal, and the balance falls faster.

Marking guide: 1 mark for the monthly rate, 2 marks per correct row (4 marks), 1 mark for the explanation.

Practise this

Sources & how we know this

Based on the official NESA syllabus. Not yet individually reviewed by a person; always check NESA and your school's materials for current rules.

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