1. © Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Pay as you earn

2. In this activity you will work out how much income tax typical workers pay.

3. Income tax 2014 - 2015 Income tax is paid on ‘taxable income’ above a certain level. Taxable income = annual income – personal tax allowance Basic Rate: 20% on the first £31 865 of taxable income How to calculate income tax Higher Rate: 40% on taxable income from £31 866 to £150 000 Additional Rate 45% on any taxable income above £150 000

4. Example Katie earns £400 per week. Her personal tax allowance is £10 000. Taxable income To calculate the income tax Katie will pay: Katie’s annual income Income Tax Think about What needs to be done first? Think about What methods could you use to work out 20%? = £400  52 = £20 800 = 20% of £10 800 = £20 800 – £10 000 = £10 800 = £2160 per annum

5. Example Liam earns £58 600 per annum. His personal tax allowance is £ 10 000. Taxable income To calculate the income tax Liam will pay: Tax at basic rate Think about What needs to be done first? Think about What income tax will Liam pay each month? = 20% of £31 865 = £58 600 – £10 000 = £48 600 = £6373 Tax at higher rate = 40% of (£48 600 – £31 865) = 40% of £16 735 = £6694 Total income tax= £6694 + £6373 = £13 067 per annum

6. Question 1 Sam earns £2275 per month. His personal tax allowance is £ 10 000. Taxable income Income tax at the basic rate = 20% of £17 300 = £27 300 – £10 000 = £17 300 = £3460 per annum Sam’s annual income = £2275  12 = £27 300

7. Question 2 Meera earns £79 800 per annum. Her personal tax allowance is £ 10 000. Taxable income Income tax at basic rate = 20% of £31 865 = £79 800 – £10 000 = £69 800 = £6373 Income tax at higher rate = 40% of (£69 800 – £31 865) = 40% of £37 935 = £15 174 Total income tax= £15 174 + £6373 = £21 547 per annum

8. Does a person who earns £30 000 per year pay twice as much tax as someone who earns £15 000 per year? Sketch a graph of income tax against taxable income. How much do you need to earn before you become a higher rate tax payer? Sketch a graph of income tax against annual earnings for earnings up to £100 000. At the end of the activity Pay as you earn

9. Taxable income Income tax on £30 000 Tax at basic rate Think about What do you need to assume? = 20% of £20 000 = £30 000 – £10 000 = £20 000 = £4000 Taxable income Income tax on £15 000 Tax at basic rate = 20% of £5000 = £15 000 – £10 000 = £5000 = £1000

10. Graph of income tax against taxable income Think about is income tax proportional to taxable income? £31 865 £6373 £150 000 £53 627 £0 Taxable income Income tax

11. Graph of income tax against annual earnings Think about How does the steepness of each line segment relate to the tax rates? £10 000 £6373 £100 000 £0 Annual earnings Income tax £29 627 £41 865