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Money models

Model a money problem by choosing what to calculate, then check the answer makes sense. Pay is the rate times the hours. Income tax is worked out in brackets: each part of the income is taxed at its own rate, so for incomes above $18 200 the rate on the last dollar (the marginal rate) is higher than the tax as a share of all the income (the effective rate).

People sometimes turn down a pay rise because it 'puts them in a higher tax bracket'. Do they lose money? A tax model answers it.

To model a money problem: say what you need to find, choose the calculation, work it out, then check the answer makes sense in the situation.

Income Rate on that part
$0 to $18 200 0%
$18 201 to $45 000 15%
$45 001 to $135 000 30%
$135 001 to $190 000 37%
over $190 000 45%

Each part of the income is taxed at its own rate. The marginal rate is the rate on the last dollar; the effective rate is all the tax as a percentage of the income.

PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.

One more dollar

Your income goes from $45 000 to $45 001, into the 30% bracket. What happens to your tax?

TryTry it on the board and compare the result with your prediction.

Tax on an income

Try it yourselfYour edits are saved in this browser.

Set the income to $60 000. Read the tax and the two rates. Was your prediction right?

Use the board. This ticks when you get there.

InvestigateWork out why it happens, one step at a time.

Marginal and effective

Here is the routine.

Worked exampleBefore each step, say what you think comes next.
  1. 60 000−45 000=15 00060\,000 - 45\,000 = 15\,000The part in the 30% bracket.

Read Jay's working. Which part of his income is in the 30% bracket?

What is the tax on an income of $30 000, in dollars?

Jay works out his tax. Click the line where his model goes wrong.

Someone earns $60 000. Why is their effective tax rate (14.2%) lower than their marginal rate (30%)?

ModifyChange the problem on purpose and see what happens.

Brackets and pay

Need a hint?

Where does the 15% bracket end?

Need a hint?

Try $90 000, then go higher.

Another hint

Watch the effective rate as the income passes $90 000.

Try it yourselfYour edits are saved in this browser.

Find the income at the top of the 15% bracket. What is the tax there?

Use the board. This ticks when you get there.

Find an income whose effective tax rate is more than 20%.

Use the board. This ticks when you get there.

A job pays $28.50 an hour. Set the board for 12 hours. What is the pay?

Use the board. This ticks when you get there.

Overtime is paid at time and a half. How much is 3 hours of overtime at a rate of $28.50, in dollars?

PractiseA few on your own, to check you have it.

Money models

What is the tax on $100 000, in dollars?

What is the effective tax rate on $100 000, as a percentage to 2 decimal places?

How could this tax model be improved to match a real tax bill?

Review: decrease $250 by 12%. What is the new amount, in dollars?

A bank account is overdrawn: its balance is −$120. Then $85 is paid in and a $40 fee is taken. What is the balance now, in dollars?

MakeMake your own problem using what you have learned. Expect a few tries; that is normal.

$50 000 to spend

Then say whether your answer makes sense, and what the model leaves out.

Try it yourselfYour edits are saved in this browser.
Need a hint?

Income after tax = income − tax.

Another hint

Try incomes between $55 000 and $60 000.

Find an income (to the nearest $1000) that leaves about $50 000 after tax: between $49 500 and $50 500.

Use the board. This ticks when you get there.

For teachers

Students model pay and income tax in brackets, compare marginal and effective rates, and judge what a simple tax model leaves out (AC9M8N05, node 2). About 40 minutes.

Open the teacher guide: answers, solutions, slides and a worksheet.

Students will be able to

Before class

Do the Run board yourself first. Students need percentage change (previous lesson).

The one idea: each part of the income is taxed at its own bracket's rate, so crossing into a higher bracket never lowers take-home pay. The common mistake is taxing the whole income at the top rate (Jay's mistake).

The board uses a simplified version of Australia's 2026–27 resident rates (0%, 15%, 30%, 37%, 45%, with thresholds $18 200, $45 000, $135 000, $190 000), without the Medicare levy or offsets. Check the ATO's current rates before quoting them as exact; the 15% rate is legislated to fall to 14% from 1 July 2027.

Wider: effective rates across incomes as a graph; superannuation contributions.

Running the lesson

  1. Predict: ask what happens to the first $45 000 when income passes it.
  2. Run: ask which rate goes up in steps and which rises smoothly.
  3. Investigate: ask Jay to split his income into parts.
  4. Modify: ask why time and a half is × 1.5.
  5. Make: ask what the model leaves out.

The hard part (on purpose)

Taxing parts, not the whole. Ask students to split the income into the bracket parts on paper before they calculate.

When students get stuck

Stretch and support

Stretch: Plot the effective rate for incomes from $20 000 to $200 000. Why does it rise smoothly when the marginal rate jumps?

Support: A table with one row per bracket: the part of the income, the rate, the tax.

Where it leads

This completes AC9M8N05.

Where it leads: financial mathematics in Years 9 and 10 (interest, budgets), and modelling with rates.

Sources

What each step is for

Now you can
Practise this skillNew questions, new numbers each timeGet 3 right in a row to mark it practised.Next lesson27. RatesA rate compares two quantities with different units: 60 km per hour, $4 per kg, 80 beats per minute. The unit rate is how much for 1 of the second quantity: divide the first by the second. A ratio compares quantities in the same units. Speeds convert with 1 km/h = 1000 m ÷ 3600 s.