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.