Mathematics Standard • Year 11 • Module 3 • Lesson 8
Calculating Income Tax
Practise HSC Mathematics Standard 2-style writing on Income Tax — short answers and one structured extended response.
Reference — 2024–25 ATO tax brackets (residents)
| Taxable income | Tax on this income |
|---|---|
| $0 – $18,200 | Nil |
| $18,201 – $45,000 | Nil + 19c for each $1 over $18,200 |
| $45,001 – $120,000 | $5,092 + 32.5c for each $1 over $45,000 |
| $120,001 – $180,000 | $29,467 + 37c for each $1 over $120,000 |
| $180,001 + | $51,667 + 45c for each $1 over $180,000 |
Medicare levy = 2% of taxable income.
1. Short-answer questions
1.1 Calculate the income tax payable on a taxable income of $56,800 using the 2024–25 ATO brackets. 2 marks Band 3
1.2 A worker has a taxable income of $92,400. Their PAYG withheld for the year was $19,800.
(a) Calculate the total tax liability (income tax + Medicare levy).
(b) State whether the worker has a refund or debt, and the amount. 3 marks Band 3-4
1.3 A worker has a taxable income of $138,200.
(a) Calculate the income tax payable.
(b) Calculate the worker's effective tax rate (income tax only, ÷ taxable income × 100), to 1 d.p.
(c) The worker claims "I'm paying 37% tax on all my income". Explain in one sentence whether this is correct or misleading. 4 marks Band 4
2. Extended response
2.1 Hugo is a high-school teacher in NSW. For the 2024–25 financial year:
Salary: $86,400 • Bank interest: $480 • Allowable deductions: $2,140 • PAYG withheld by employer: $18,650.
(a) Calculate Hugo's taxable income.
(b) Calculate his income tax payable and Medicare levy.
(c) State whether Hugo receives a refund or owes a debt, by how much, and explain in one sentence whether the size of the difference (relative to PAYG withheld) suggests his withholding was approximately correct for the year. 7 marks Band 5-6
Explicit marking criteria
Part (a) — 1 mark
• 1 mark — correct taxable income = gross (salary + interest) − deductions.
Part (b) — 3 marks
• 1 mark — correctly identifies the bracket and writes the bracket formula.
• 1 mark — correct income tax to the cent.
• 1 mark — correct Medicare levy = taxable income × 0.02.
Part (c) — 3 marks
• 1 mark — correctly compares PAYG to total liability and states refund or debt.
• 1 mark — explicit conclusion sentence naming refund/debt and dollar amount.
• 1 mark — brief, accurate comment on the size of the difference relative to PAYG withheld (e.g. less than 5% of PAYG implies withholding was close).
Your response:
Stuck on (c)? After computing the refund or debt, divide the amount by the PAYG figure — small percentage means the withholding was a reasonable estimate.How did this worksheet feel?
What I'll revisit before next class:
1.1 — Income tax on $56,800 (2 marks)
Sample response.
$56,800 is in the $45,001 – $120,000 bracket.
Income tax = $5,092 + 0.325 × ($56,800 − $45,000) = $5,092 + 0.325 × $11,800 = $5,092 + $3,835 = $8,927.00.
Marking notes. 1 mark — correctly applies the bracket formula with substitution shown. 1 mark — correct numerical answer with units. A bare "$8,927" with no working scores 1/2 even if numerically correct.
1.2 — Total liability + refund or debt (3 marks)
Sample response.
(a) Income tax = $5,092 + 0.325 × ($92,400 − $45,000) = $5,092 + $15,405 = $20,497. Medicare = $92,400 × 0.02 = $1,848. Total liability = $22,345.00.
(b) $19,800 < $22,345 → tax debt of $2,545.00.
Marking notes. 1 mark — correct income tax. 1 mark — correct Medicare levy and total liability. 1 mark — correct comparison and conclusion sentence naming debt and amount. Common error: stating "refund of $2,545" — direction of comparison is wrong.
1.3 — Marginal vs effective rate (4 marks)
(a) Sample response. $138,200 in $120,001 – $180,000 bracket. Income tax = $29,467 + 0.37 × ($138,200 − $120,000) = $29,467 + 0.37 × $18,200 = $29,467 + $6,734 = $36,201.00.
(b) Sample response. Effective rate = $36,201 ÷ $138,200 × 100 ≈ 26.2%.
(c) Sample response. The claim is misleading. The 37% rate is the marginal rate — it only applies to the $18,200 above $120,000. The lower portions of income are taxed at 0%, 19% and 32.5%, so the worker's average (effective) tax rate is only 26.2%.
Marking notes. (a) 1 mark — correct bracket formula and result. (b) 1 mark — correct effective rate using income tax only. (c) 1 mark — identifies the claim as misleading. 1 mark — gives the marginal-vs-effective distinction (must reference that 37% applies only above $120,000). A response saying only "wrong" scores 0/1.
2.1 — Hugo's full tax return (7 marks): sample Band-6 response with annotations
Sample Band-6 response.
(a) Taxable income.
Gross income = $86,400 + $480 = $86,880.
Taxable income = $86,880 − $2,140 = $84,740. [1 mark — correct taxable income.]
(b) Income tax and Medicare levy.
$84,740 is in the $45,001 – $120,000 bracket. [1 mark — identifies bracket and writes the formula.]
Income tax = $5,092 + 0.325 × ($84,740 − $45,000) = $5,092 + 0.325 × $39,740 = $5,092 + $12,915.50 = $18,007.50. [1 mark — correct income tax.]
Medicare levy = $84,740 × 0.02 = $1,694.80. [1 mark — correct Medicare levy.]
(c) Refund or debt + reasonableness.
Total tax liability = $18,007.50 + $1,694.80 = $19,702.30.
PAYG $18,650 < liability $19,702.30 → tax debt = $19,702.30 − $18,650 = $1,052.30. [1 mark — correct comparison and direction.]
Conclusion: Hugo has a tax debt of $1,052.30. [1 mark — explicit conclusion naming debt + dollar amount.]
Reasonableness check: $1,052.30 ÷ $18,650 ≈ 5.6% of PAYG withheld. This is a small percentage, so the employer's withholding was reasonably close to the actual liability — the debt likely reflects the small bank interest and the allowable deductions which the employer didn't account for in PAYG estimates. [1 mark — brief, accurate reasonableness comment.]
Total: 7/7.
Band descriptors for marker.
Band 3: Calculates taxable income and attempts brackets, but either applies brackets to gross income or omits Medicare. ≈ 3 marks.
Band 4: Taxable income, income tax and Medicare all correct; total liability correct; misses the refund/debt direction OR omits the conclusion sentence. ≈ 5 marks.
Band 5: Full numerical solution including refund/debt with sentence, but no reasonableness comment in (c). ≈ 6 marks.
Band 6: All numerical steps correct, conclusion sentence present, AND a brief reasonableness comment relating the debt size to the PAYG estimate. 7/7.