1. Nuffield Mathematics Activity
Pay as you earn

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

3. Income tax
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 £ of taxable income
Higher Rate: 40% on taxable income from £ to £
Additional Rate 45% on any taxable income above £

4. Her personal tax allowance is £11 500.
Example
Katie earns £400 per week.
Her personal tax allowance is £
To calculate the income tax Katie will pay:
Think about What needs to be done first?
Katie’s annual income
= £400  52
= £20 800
Taxable income
= £ – £11 500
= £9300
Think about What methods could you use to work out 20%?
Income Tax
= 20% of £9300
= £1860 per annum

5. His personal tax allowance is £11 500.
Example
Liam earns £ per annum.
His personal tax allowance is £
To calculate the income tax Liam will pay:
Taxable income
= £ – £11 500
Think about What needs to be done first?
= £47 100
Tax at basic rate
= 20% of £33 500
= £6700
Tax at higher rate
= 40% of (£ – £33 500)
= 40% of £13 600
= £5440
Think about What income tax will Liam pay each month?
Total income tax
= £ £6700
= £ per annum

6. Question 1
Sam earns £2275 per month.
His personal tax allowance is £
Sam’s annual income
= £2275  12
= £27 300
Taxable income
= £ – £11 500
= £15 800
Income tax at the basic rate
= 20% of £15 800
= £3160 per annum

7. Question 2
Meera earns £ per annum.
Her personal tax allowance is £
Taxable income
= £ – £11 500
= £68 300
Income tax at basic rate
= 20% of £33 500
= £6700
Income tax at higher rate
= 40% of (£ – £33 500)
= 40% of £34 800
= £13 920
Total income tax
= £ £6700
= £ per annum

8. Pay as you earn At the end of the activity
Does a person who earns £ per year pay twice as much tax as someone who earns £ 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 £

9. Income tax on £30 000 Taxable income = £30 000 – £11 500 = £18 500
Think about What do you need to assume?
Taxable income
= £ – £11 500
= £18 500
Tax at basic rate
= 20% of £18 500
= £3700
Income tax on £15 000
Taxable income
= £ – £11 500
= £3500
Tax at basic rate
= 20% of £3500
= £700

10. Graph of income tax against taxable income£0
Taxable income
Income tax
£53 300
Think about Is income tax proportional to taxable income?
£6700
£33 500 £

11. Graph of income tax against annual earnings£0
Annual earnings
Income tax
Think about How does the steepness of each line segment relate to the tax rates?
£28 700
£6700
£11 500
£45 000 £