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
= £6860Total 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
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