© 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 Income tax is paid on ‘taxable income’ above a certain level. Taxable income = annual income – personal tax allowance Basic Rate: 20% on the first £ of taxable income How to calculate income tax Higher Rate: 40% on taxable income from £ to £ Additional Rate 45% on any taxable income above £

Example Katie earns £400 per week. Her personal tax allowance is £ Taxable income To calculate the income tax Katie will pay: Katie’s annual income Income Tax Think about What needs to be done first? Think about What methods could you use to work out 20%? = £400  52 = £ = 20% of £ = £ – £ = £ = £2160 per annum

Example Liam earns £ per annum. His personal tax allowance is £ Taxable income To calculate the income tax Liam will pay: Tax at basic rate Think about What needs to be done first? Think about What income tax will Liam pay each month? = 20% of £ = £ – £ = £ = £6373 Tax at higher rate = 40% of (£ – £31 865) = 40% of £ = £6694 Total income tax= £ £6373 = £ per annum

Question 1 Sam earns £2275 per month. His personal tax allowance is £ Taxable income Income tax at the basic rate = 20% of £ = £ – £ = £ = £3460 per annum Sam’s annual income = £2275  12 = £27 300

Question 2 Meera earns £ per annum. Her personal tax allowance is £ Taxable income Income tax at basic rate = 20% of £ = £ – £ = £ = £6373 Income tax at higher rate = 40% of (£ – £31 865) = 40% of £ = £ Total income tax= £ £6373 = £ per annum

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 £ At the end of the activity Pay as you earn

Taxable income Income tax on £ Tax at basic rate Think about What do you need to assume? = 20% of £ = £ – £ = £ = £4000 Taxable income Income tax on £ Tax at basic rate = 20% of £5000 = £ – £ = £5000 = £1000

Graph of income tax against taxable income Think about is income tax proportional to taxable income? £ £6373 £ £ £0 Taxable income Income tax

Graph of income tax against annual earnings Think about How does the steepness of each line segment relate to the tax rates? £ £6373 £ £0 Annual earnings Income tax £ £41 865