© 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 2014 - 2015Income tax is paid on ‘taxable income’ above a certain level.

Taxable income = annual income – personal tax allowance

Basic Rate:20% on the first £31 865 of taxable income

How to calculate income tax

Higher Rate:40% on taxable income from £31 866 to £150 000

Additional Rate45% on any taxable income above £150 000

Example Katie earns £400 per week. Her personal tax allowance is £10 000.

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 £10 800

= £20 800 – £10 000

= £10 800

= £2160 per annum

Example Liam earns £58 600 per annum. His personal tax allowance is £ 10 000.

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 £31 865

= £58 600 – £10 000

= £48 600

= £6373

Tax at higher rate = 40% of (£48 600 – £31 865)= 40% of £16 735

= £6694

Total income tax = £6694 + £6373

= £13 067 per annum

Question 1 Sam earns £2275 per month. His personal tax allowance is £ 10 000.

Taxable income

Income tax at the basic rate = 20% of £17 300

= £27 300 – £10 000

= £17 300

= £3460 per annum

Sam’s annual income = £2275 12

= £27 300

Question 2 Meera earns £79 800 per annum. Her personal tax allowance is £ 10 000.

Taxable income

Income tax at basic rate = 20% of £31 865

= £79 800 – £10 000

= £69 800

= £6373

Income tax at higher rate= 40% of (£69 800 – £31 865)= 40% of £37 935

= £15 174Total income tax = £15 174 + £6373

= £21 547 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 £20 000

= £30 000 – £10 000

= £20 000

= £4000

Taxable income

Income tax on £15 000

Tax at basic rate = 20% of £5000

= £15 000 – £10 000

= £5000

= £1000

Graph of income tax against taxable income

Think aboutis income tax proportional to taxable income?

£31 865

£6373

£150 000

£53 627

£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?

£10 000

£6373

£100 000 £0 Annual earnings

Income tax

£29 627

£41 865