Pay as you earn
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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 2012 - 2013. Income tax is paid on ‘taxable income’ above a certain level. How to calculate income tax.

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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 2012 - 2013

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 £34 370 of taxable income

Higher Rate:40% on taxable income between £34 370 and £150 000

Additional Rate50% on any taxable income above £150 000


Example

Katie earns £400 per week.

Her personal tax allowance is £8105.

To calculate the income tax Katie will pay:

Think aboutWhat needs to be done first?

Katie’s annual income

= £400  52

= £20 800

Taxable income

= £20 800 – £8105

= £12 695

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

Income Tax

= 20% of £12 695

= £2539 per annum


Example

Liam earns £58 600 per annum.

His personal tax allowance is £8105.

To calculate the income tax Liam will pay:

Taxable income

= £58 600 – £8105

Think aboutWhat needs to be done first?

= £50 495

Tax at basic rate

= 20% of £34 370

= £6874

Tax at higher rate

= 40% of (£50 495 – £34 370)

= 40% of £16 125

= £6450

Think aboutWhat income tax will Liam pay each month?

Total income tax

= £6874 + £6450

= £13 324 per annum


Question 1

Sam earns £2275 per month.

His personal tax allowance is £8105.

Sam’s annual income

= £2275  12

= £27 300

Taxable income

= £27 300 – £8105

= £19 195

= 20% of £19 195

Income tax at the basic rate

= £3839 per annum


Question 2

Meera earns £79 800 per annum.

His personal tax allowance is £8105.

Taxable income

= £79 800 – £8105

= £71 695

Income tax at basic rate

= 20% of £34 370

= £6874

Income tax at higher rate

= 40% of (£71 695 – £34 370)

= 40% of £37 325

= £14 930

Total income tax

= £6874 + £14 930

= £21 804 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 earningsfor earnings up to £100 000.


Income tax on £30 000

Think aboutWhat do you need to assume?

Taxable income

= £30 000 – £8105

= £21 895

Tax at basic rate

= 20% of £21 895

= £4379

Income tax on £15 000

Taxable income

= £15 000 – £8105

= £6895

Tax at basic rate

= 20% of £6895

= £1379


Graph of income tax against taxable income

Income tax

£53 126

Think aboutis income tax proportional to taxable income?

£6874

£0

Taxable income

£150 000

£34 370


Graph of income tax against annual earnings

Income tax

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

£29 884

£6874

£100 000

£8105

£42 475

£0

Annual earnings


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