Year 9 Maths Advanced Earning Money

Income Tax

20 practice questions 1 video lesson Theory + worked examples

Income tax is worked out on taxable income: gross income minus allowable deductions. This NSW Year 9 Advanced maths subtopic uses an Australian resident tax table and the $2\%$ Medicare levy (NESA outcome MA5‑FIN‑C‑01).

You will find taxable income from wages, interest and dividends, calculate tax from the right band of the table, and add the Medicare levy. You will compare the tax owed with the tax withheld to find a refund or an amount owing, find an average tax rate, explain why a pay rise is taxed at the top rate, and work backwards from total tax to income. It is part of Year 9 Advanced Earning Money.

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Income Tax - Video - Income Tax Watch

Theory

Income tax is worked out on taxable income: all income less allowable deductions. A tax table taxes each slice of income at its own rate, and most people also pay a Medicare levy of $2\%$. This Year 9 Advanced maths page covers using the table, refunds and amounts owing, average and marginal tax rates, and working backwards from the tax.

Gross income is all income before tax: wages or salary, plus interest, dividends, freelance work and so on.

Allowable deductions are work-related costs and gifts the tax rules allow you to subtract, such as union fees, uniforms, tools and donations to charity.

Taxable income $=$ gross income $-$ allowable deductions. Cents are usually ignored.

A tax table sets the tax for each bracket of income. Each rate applies only to the dollars within that bracket, so earning more never leaves you worse off after tax.

The Medicare levy is $2\%$ of taxable income for most taxpayers. PAYG tax is withheld from pay during the year; at tax time the total is compared with the tax payable to give a refund or an amount owing.

Tax rates apply to slices of income. Moving into a higher bracket only changes the tax on the dollars in that bracket.

Work out the taxable income first, then the tax and levy, then compare with the PAYG tax already withheld.

Tax table used on this page (2026–27 resident rates):

Taxable income	Tax payable
$\$0$–$\$18\,200$	Nil
$\$18\,201$–$\$45\,000$	$15$c for each $\$1$ over $\$18\,200$
$\$45\,001$–$\$135\,000$	$\$4020$ plus $30$c for each $\$1$ over $\$45\,000$
$\$135\,001$–$\$190\,000$	$\$31\,020$ plus $37$c for each $\$1$ over $\$135\,000$
$\$190\,001$ and over	$\$51\,370$ plus $45$c for each $\$1$ over $\$190\,000$

\[\text{taxable income} = \text{gross income} - \text{deductions}\]

taxable = gross - deductions

\[\text{refund} = \text{PAYG withheld} - (\text{tax} + \text{Medicare levy})\]

refund = PAYG - (tax + levy)

Average tax rate. $\dfrac{\text{tax}}{\text{taxable income}}\times 100\%$.

Marginal tax rate. The rate on the next dollar earned: the rate of the bracket the income is in. A pay rise inside one bracket is taxed at that rate.

How to calculate income tax

Add all the income for the year: convert weekly or fortnightly pay to a year, and include interest and other income.
Subtract the allowable deductions to get the taxable income; drop any cents.
Find the row of the tax table, subtract the bracket's starting amount, multiply by the rate and add the base amount.
Add the Medicare levy if asked, and compare with the PAYG tax withheld.

Harder problems

Refund or owing: PAYG withheld more than tax payable means a refund (Example 2).
Pay rise or extra deduction: work out the tax at both incomes and subtract. If the change crosses a bracket boundary, part is at one rate and part at the other.
Splitting income: two people each earning half usually pay less in total than one person earning it all, because more of the income falls in the lower brackets.
Working backwards: find which row the tax falls in by testing the row's end points, then solve a linear equation (Example 4). With the levy included, the equation has two terms in $x$.
Tax per pay: yearly tax $\div 12$ for monthly, $\div 26$ for fortnightly, $\div 52$ for weekly.

Example 1 — Taxable income from several sources

Ava earns a wage of $\$1185$ a week for $52$ weeks and $2.8\%$ interest on $\$15\,000$ in savings. Her deductions are uniforms $\$380$, union fees $\$610$ and a donation $\$150$. Use the tax table and a $2\%$ Medicare levy to find
(i) her taxable income
(ii) her tax
(iii) her Medicare levy
(iv) the total.

Solution

$\text{wage}$	$=$	$1185\times 52 = \$61\,620$
$\text{interest}$	$=$	$0.028\times 15\,000 = \$420$
$\text{deductions}$	$=$	$380+610+150 = \$1140$
$\text{(i) taxable}$	$=$	$61\,620+420-1140$
	$=$	$\mathbf{\$60\,900}$

This is in the third row of the table.

$\text{(ii) tax}$	$=$	$4020+0.30\times(60\,900-45\,000)$
	$=$	$4020+4770 = \mathbf{\$8790}$
$\text{(iii) levy}$	$=$	$0.02\times 60\,900 = \mathbf{\$1218}$
$\text{(iv) total}$	$=$	$8790+1218 = \mathbf{\$10\,008}$

4020 + 0.30 \times 15900 = 8790

Example 2 — Refund or tax owing?

Raj's taxable income is $\$112\,400$. His employer withheld $\$28\,300$ in PAYG tax during the year. With a Medicare levy of $2\%$, does he get a refund or owe tax, and how much?

Solution

$\$112\,400$ is in the third row.

$\text{tax}$	$=$	$4020+0.30\times(112\,400-45\,000)$
	$=$	$4020+20\,220 = \$24\,240$
$\text{levy}$	$=$	$0.02\times 112\,400 = \$2248$
$\text{total payable}$	$=$	$24\,240+2248 = \$26\,488$
$\text{PAYG} - \text{payable}$	$=$	$28\,300-26\,488 = \$1812$

28300 - 26488 = 1812

He paid more than he owes, so he gets a refund of $\$1812$.

Example 3 — Average and marginal rates

(i) Find the tax on a taxable income of $\$140\,000$.
(ii) Find the average tax rate, correct to two decimal places.
(iii) How much extra tax is paid on a $\$2000$ pay rise?

Solution

$\text{(i) tax}$	$=$	$31\,020+0.37\times(140\,000-135\,000)$
	$=$	$31\,020+1850 = \mathbf{\$32\,870}$
$\text{(ii) average}$	$=$	$\dfrac{32\,870}{140\,000}\times 100\%$
	$=$	$23.478\ldots\% \approx \mathbf{23.48\%}$
$\text{(iii) extra}$	$=$	$0.37\times 2000 = \mathbf{\$740}$

\frac{32870}{140000} \times 100 = 23.48

The extra $\$2000$ is all in the $37$c bracket, so it is taxed at the marginal rate of $37\%$, much more than the average of about $23\%$.

Example 4 — Working back from the tax

Noah paid $\$11\,220$ in income tax (not counting the Medicare levy). Find his taxable income.

Solution

First decide which row. The third row covers tax from $\$4020$ (at $\$45\,000$) to $\$31\,020$ (at $\$135\,000$), and $\$11\,220$ is between these. Let the income be $\$x$.

$4020+0.30(x-45\,000)$	$=$	$11\,220$
$0.30(x-45\,000)$	$=$	$7200$
$x-45\,000$	$=$	$24\,000$
$x$	$=$	$\mathbf{69\,000}$

0.30 (x - 45000) = 7200

Check: $\$69\,000$ is in the third row, and $4020+0.30\times 24\,000 = \$11\,220$ ✓

Common pitfalls

Subtract the start of the bracket. For $\$60\,900$, tax is $4020+0.30\times(60\,900-45\,000)$, not $0.30\times 60\,900$.

Deductions come off first. Use taxable income, after deductions, both in the tax table and for the Medicare levy.

A higher bracket does not tax everything. Moving above $\$135\,000$ only taxes the dollars above $\$135\,000$ at $37$c.

Refund or owing? If PAYG withheld is more than the tax payable, the difference is a refund; if it is less, the difference is owed.

Frequently asked questions

How do you calculate taxable income?

Add all income for the year, including wages, interest and other earnings, then subtract the allowable deductions such as work expenses and donations.

How do you use a tax table?

Find the row that contains the taxable income. Subtract the lower limit of that row, multiply by the rate in cents per dollar, and add the fixed amount shown for the row.

What is the Medicare levy?

A charge that helps fund the public health system. In these questions it is $2\%$ of taxable income, added to the income tax.

What is the difference between marginal and average tax rate?

The marginal rate is the rate on the next dollar earned. The average rate is the total tax divided by the taxable income, which is lower because the first slices are taxed less.

Can a pay rise leave you worse off after tax?

No. A higher rate only applies to the extra dollars in the higher bracket, so you always keep part of a pay rise.

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PAYG and Net Pay

Taxable income	Tax payable
\(\$0\)–\(\$18\,200\)	Nil
\(\$18\,201\)–\(\$45\,000\)	\(15\)c for each \(\$1\) over \(\$18\,200\)
\(\$45\,001\)–\(\$135\,000\)	\(\$4020\) plus \(30\)c for each \(\$1\) over \(\$45\,000\)
\(\$135\,001\)–\(\$190\,000\)	\(\$31\,020\) plus \(37\)c for each \(\$1\) over \(\$135\,000\)
\(\$190\,001\) and over	\(\$51\,370\) plus \(45\)c for each \(\$1\) over \(\$190\,000\)

\(\text{wage}\)	\(=\)	\(1185\times 52 = \$61\,620\)
\(\text{interest}\)	\(=\)	\(0.028\times 15\,000 = \$420\)
\(\text{deductions}\)	\(=\)	\(380+610+150 = \$1140\)
\(\text{(i) taxable}\)	\(=\)	\(61\,620+420-1140\)
\(\)	\(=\)	\(\mathbf{\$60\,900}\)

\(\text{(ii) tax}\)	\(=\)	\(4020+0.30\times(60\,900-45\,000)\)
\(\)	\(=\)	\(4020+4770 = \mathbf{\$8790}\)
\(\text{(iii) levy}\)	\(=\)	\(0.02\times 60\,900 = \mathbf{\$1218}\)
\(\text{(iv) total}\)	\(=\)	\(8790+1218 = \mathbf{\$10\,008}\)

\(\text{tax}\)	\(=\)	\(4020+0.30\times(112\,400-45\,000)\)
\(\)	\(=\)	\(4020+20\,220 = \$24\,240\)
\(\text{levy}\)	\(=\)	\(0.02\times 112\,400 = \$2248\)
\(\text{total payable}\)	\(=\)	\(24\,240+2248 = \$26\,488\)
\(\text{PAYG} - \text{payable}\)	\(=\)	\(28\,300-26\,488 = \$1812\)

\(\text{(i) tax}\)	\(=\)	\(31\,020+0.37\times(140\,000-135\,000)\)
\(\)	\(=\)	\(31\,020+1850 = \mathbf{\$32\,870}\)
\(\text{(ii) average}\)	\(=\)	\(\dfrac{32\,870}{140\,000}\times 100\%\)
\(\)	\(=\)	\(23.478\ldots\% \approx \mathbf{23.48\%}\)
\(\text{(iii) extra}\)	\(=\)	\(0.37\times 2000 = \mathbf{\$740}\)

\(4020+0.30(x-45\,000)\)	\(=\)	\(11\,220\)
\(0.30(x-45\,000)\)	\(=\)	\(7200\)
\(x-45\,000\)	\(=\)	\(24\,000\)
\(x\)	\(=\)	\(\mathbf{69\,000}\)

Income Tax

📖 Theory

How to calculate income tax

Harder problems

Common pitfalls

Frequently asked questions

Theory