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

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

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© Nuffield Foundation 2011

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 2013 - 2014Income tax is paid on ‘taxable income’ above a certain level.

Taxable income = annual income – personal tax allowance

Basic Rate:20% on the first £32 010 of taxable income

How to calculate income tax

Higher Rate:40% on taxable income between £32 010 and £150 000

Additional Rate45% on any taxable income above £150 000

Example Katie earns £400 per week. Her personal tax allowance is £9440.

Taxable income

To calculate the income tax Katie will pay:

Katie’s annual income

Income Tax

Think aboutWhat needs to be done first?

Think aboutWhat methods could you use to work out 20%?

= £400 52

= £20 800

= 20% of £11 360

= £20 800 – £9440

= £11 360

= £2272 per annum

Example Liam earns £58 600 per annum. His personal tax allowance is £9440.

Taxable income

To calculate the income tax Liam will pay:

Tax at basic rate

Think aboutWhat needs to be done first?

Think aboutWhat income tax will Liam pay each month?

= 20% of £32 010

= £58 600 – £9440

= £49 160

= £6402

Tax at higher rate = 40% of (£49 160 – £32 010)= 40% of £17 150

= £6860

Total income tax = £6860 + £6402

= £13 262 per annum

Question 1 Sam earns £2275 per month. His personal tax allowance is £9440.

Taxable income

Income tax at the basic rate = 20% of £17 860

= £27 300 – £9440

= £17 860

= £3572 per annum

Sam’s annual income = £2275 12

= £27 300

Question 2 Meera earns £79 800 per annum. Her personal tax allowance is £9440.

Taxable income

Income tax at basic rate = 20% of £32 010

= £79 800 – £9440

= £70 360

= £6402

Income tax at higher rate= 40% of (£70 360 – £32 010)= 40% of £38 350

= £15 340Total income tax = £15 340 + £6402

= £21 742 per annum

• 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.

At the end of the activity

Pay as you earn

Taxable income

Income tax on £30 000

Tax at basic rate

Think aboutWhat do you need to assume?

= 20% of £20 560

= £30 000 – £9440

= £20 560

= £4112

Taxable income

Income tax on £15 000

Tax at basic rate = 20% of £5560

= £15 000 – £9440

= £5560

= £1112

Graph of income tax against taxable income

Think aboutis income tax proportional to taxable income?

£32 010

£6402

£150 000

£53 598

£0 Taxable income

Income tax

Graph of income tax against annual earnings

Think aboutHow does the steepness of each line segment relate to the tax rates?

£9440

£6402

£100 000 £0 Annual earnings

Income tax

£29 822

£41 450