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# Pay as you earn

Nuffield Free-Standing Mathematics Activity. Pay as you earn. In this activity you will work out how much income tax typical workers pay. Income tax 2014 - 2015. Income tax is paid on ‘taxable income’ above a certain level. How to calculate income tax.

## Pay as you earn

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1. 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. How to calculate income tax Taxable income = annual income – personal tax allowance Basic Rate:20% on the first £31 865 of taxable income Higher Rate:40% on taxable income from £31 866 to £150 000 Additional Rate45% on any taxable income above £150 000

4. Example Katie earns £400 per week. Her personal tax allowance is £10000. To calculate the income tax Katie will pay: Think aboutWhat needs to be done first? Katie’s annual income = £400  52 = £20 800 Taxable income = £20 800 – £10000 = £10 800 Think aboutWhat methods could you use to work out 20%? Income Tax = 20% of £10 800 = £2160 per annum

5. Example Liam earns £58 600 per annum. His personal tax allowance is £ 10000. To calculate the income tax Liam will pay: Taxable income = £58 600 – £10000 Think aboutWhat needs to be done first? = £48 600 Tax at basic rate = 20% of £31 865 = £6373 Tax at higher rate = 40% of (£48 600 – £31 865) = 40% of £16 735 = £6694 Think aboutWhat income tax will Liam pay each month? Total income tax = £6694 + £6373 = £13 067 per annum

6. Question 1 Sam earns £2275 per month. His personal tax allowance is £ 10000. Sam’s annual income = £2275  12 = £27 300 Taxable income = £27 300 – £10000 = £17 300 = 20% of £17 300 Income tax at the basic rate = £3460 per annum

7. Question 2 Meera earns £79 800 per annum. Her personal tax allowance is £ 10000. Taxable income = £79 800 – £10000 = £69 800 Income tax at basic rate = 20% of £31 865 = £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. Pay as you earn At the end of the activity • 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 earningsfor earnings up to £100 000.

9. Income tax on £30 000 Think aboutWhat do you need to assume? Taxable income = £30 000 – £10000 = £20 000 Tax at basic rate = 20% of £20 000 = £4000 Income tax on £15 000 Taxable income = £15 000 – £10000 = £5000 Tax at basic rate = 20% of £5000 = £1000

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

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

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