--- title: "Money models" subtitle: "Number Foundations · Modelling · Lesson 26" --- # Money models **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** 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. :::teacher-note **In one sentence:** 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). **Students should be able to say:** I can work out income tax across brackets. I can explain the difference between the marginal and effective rate. I can model pay with a rate, hours and overtime, and check the answer makes sense. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict :::keep-together **Your income goes from $45 000 to $45 001, into the 30% bracket. What happens to your tax?** ☐ You pay less tax ☐ Nothing changes ☐ It goes up 30 cents: only the extra dollar is taxed at 30% ☐ All $45 001 is now taxed at 30% My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** It goes up 30 cents. Only the part above $45 000 is taxed at 30%; the rest is taxed as before. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Marginal and effective :::keep-together ### Tax on $30 000 Here is the routine. 1. $60\,000 - 45\,000 = 15\,000$ — The part in the 30% bracket. 2. $26\,800 \times 0.15 = 4020$ — The part from $18 200 to $45 000, at 15%. 3. $15\,000 \times 0.30 = 4500$ — The top part, at 30%. 4. $4020 + 4500 = 8520$ — Add the parts: the tax. 5. $8520 \div 60\,000 = 14.2\%$ — The effective rate. **What is the tax on an income of $30 000, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1770 30 000 − 18 200 = 11 800, and 15% of 11 800 = $1770. ::: :::keep-together ### Find the mistake **Jay works out his tax. Click the line where his model goes wrong.** ``` 1 Jay earns $50 000 a year. 2 His income reaches the 30% bracket. 3 So his tax is 30% of $50 000, which is $15 000. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: only the part above $45 000 is taxed at 30%. Tax = 15% of 26 800 + 30% of 5000 = 4020 + 1500 = $5520. ::: :::keep-together ### Two rates **Someone earns $60 000. Why is their effective tax rate (14.2%) lower than their marginal rate (30%)?** ☐ Because of the Medicare levy ☐ Effective rates are always half the marginal rate ☐ The marginal rate is wrong ☐ Most of their income is taxed at 0% or 15%; only the top part is taxed at 30% ::: :::teacher-note **Answer:** Most of their income is taxed at 0% or 15%; only the top part is taxed at 30% The lower brackets pull the average down. ::: :::typical ## Brackets and pay **The 15% bracket.** **Over 20%.** **Pay.** **Overtime.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Money models :::keep-together ### Tax on $100 000 **What is the tax on $100 000, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 20520 4020 + 30% of 55 000 = 4020 + 16 500 = $20 520. ::: :::keep-together ### Effective rate **What is the effective tax rate on $100 000, as a percentage to 2 decimal places?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 20.52 20 520 ÷ 100 000 = 20.52%. ::: :::keep-together ### Improve the model **How could this tax model be improved to match a real tax bill?** ☐ Remove the tax-free part ☐ Use one rate for everyone ☐ Add the Medicare levy and tax offsets ☐ Tax everything at the top rate ::: :::teacher-note **Answer:** Add the Medicare levy and tax offsets The model leaves out the Medicare levy (usually 2%) and offsets, so real tax is a bit different. ::: :::keep-together ### Review: decrease **Review: decrease $250 by 12%. What is the new amount, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 220 250 × 0.88 = $220. ::: :::keep-together ### An overdrawn account **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?** Answer: {{field-15}} ::: :::teacher-note **Answer:** -75 −120 + 85 − 40 = −75: still overdrawn, by $75. ::: ## Make: $50 000 to spend Then say whether your answer makes sense, and what the model leaves out. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Tax is 0% on the first $18 200 of income, 15% on the next part up to $45 000, and 30% on the part from $45 000 to $135 000. Find the tax on $50 000.** {{lines-3}} ::: :::teacher-note **Answer:** 15% of (45 000 − 18 200) = 15% of 26 800 = $4020, plus 30% of 5000 = $1500: $5520 in all. :::