Nuffield Free-Standing Mathematics Activity
Pay as you earn
© Nuffield Foundation 2011
In this activity you
will work out how
much income tax
typical workers pay.
Income tax 2013 - 2014
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 £32 010 of taxable income
Higher Rate:
40% on taxable income between £32 010 and £150 000
Additional Rate
45% on any taxable income above £150 000
Example Katie earns £400 per week.
Her personal tax allowance is £9440.
To calculate the income tax Katie will pay:
Katie’s annual income = £400  52
Think about
What needs to
be done first?
= £20 800
Taxable income = £20 800 – £9440
= £11 360
Income Tax = 20% of £11 360
= £2272 per annum
Think about
What methods could you
use to work out 20%?
Example Liam earns £58 600 per annum.
His personal tax allowance is £9440.
To calculate the income tax Liam will pay:
Taxable income = £58 600 – £9440
= £49 160
Think about
What needs to
be done first?
Tax at basic rate = 20% of £32 010
= £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
Think about
What income tax will
Liam pay each month?
Question 1
Sam earns £2275 per month.
His personal tax allowance is £9440.
Sam’s annual income = £2275  12
= £27 300
Taxable income = £27 300 – £9440
= £17 860
Income tax at the basic rate = 20% of £17 860
= £3572 per annum
Question 2
Meera earns £79 800 per annum.
Her personal tax allowance is £9440.
Taxable income = £79 800 – £9440
= £70 360
Income tax at basic rate = 20% of £32 010
= £6402
Income tax at higher rate = 40% of (£70 360 – £32 010)
= 40% of £38 350
= £15 340
Total income tax = £15 340 + £6402
= £21 742 per annum
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 earnings
for earnings up to £100 000.
Income tax on £30 000
Taxable income = £30 000 – £9440
= £20 560
Tax at basic rate = 20% of £20 560
= £4112
Income tax on £15 000
Taxable income = £15 000 – £9440
= £5560
Tax at basic rate = 20% of £5560
= £1112
Think about
What do you need
to assume?
Graph of income tax against taxable income
Income tax
£53 598
Think about
is income tax proportional
to taxable income?
£6402
£0
£32 010
£150 000
Taxable income
Graph of income tax against annual earnings
Income tax
Think about
How does the steepness
of each line segment
relate to the tax rates?
£29 822
£6402
£0 £9440
£41 450
£100 000 Annual earnings