Tax — Core Maths Compendium

Build it up, step by step

Understanding tax

Click each step below to reveal it — work through them in order the first time round.

Step 1 · The personal allowance

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Most UK taxpayers get a personal allowance — an amount of income they can earn each year before paying any income tax at all. Only income above the personal allowance is taxed.

Step 2 · Tax bands

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Once income exceeds the personal allowance, it's taxed in bands, each with its own rate (e.g. basic rate, higher rate, additional rate). Crucially, each rate only applies to the portion of income that falls within that band — not to your whole income. This is why higher earners don't pay a bigger rate on all their income, just the top slice.

Step 3 · Calculating tax owed

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To find total tax: work out how much income falls into each band (above the personal allowance), multiply each portion by its rate, then add the amounts together. In the exam you'll be given the allowance and band thresholds/rates to use — the skill is applying them correctly, slice by slice.

Step 4 · Other deductions and net pay

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Employees also usually pay National Insurance (a separate deduction) alongside income tax. Net (take-home) pay = gross income − income tax − National Insurance − any other deductions (e.g. pension contributions).

Worked example

Using a personal allowance of £12,570, a basic rate of 20% on income from £12,571 to £50,270, and a higher rate of 40% above £50,270, calculate the income tax owed on a salary of £45,000.

Taxable income = 45000 − 12570 = 32,430 (all within the basic rate band, since 45000 < 50270).
Tax = 32430 × 0.20 = £6,486.

Test yourself

Past-paper style question

Using a personal allowance of £12,570, a basic rate of 20% on income between £12,571 and £50,270, and a higher rate of 40% on income above £50,270, calculate the income tax owed by someone earning £58,000 in a year. [4 marks]

Show the answer

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Amount taxed at basic rate = 50270 − 12570 = 37,700. Tax at 20% = 37700×0.20 = £7,540.

Amount taxed at higher rate = 58000 − 50270 = 7,730. Tax at 40% = 7730×0.40 = £3,092.

Total tax = 7540+3092 = £10,632.

Practice

Tax worksheet

Five short questions on tax. Work through them, then reveal the mark scheme to check.

Using the rates above, calculate the tax owed on a salary of £20,000.
Calculate the tax owed on a salary of £12,000.
Calculate the tax owed on a salary of £70,000.
Two employees earn £30,000 and £40,000. Find the difference in tax they each pay.
Explain why doubling your salary from £40,000 to £80,000 more than doubles the amount of tax you pay.

Mark scheme

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Taxable = 20000−12570 = 7,430. Tax = 7430×0.20 = £1,486.
Salary is below the personal allowance (£12,570), so no tax is owed — £0.
Basic band tax = (50270−12570)×0.20 = 37700×0.20 = £7,540. Higher band tax = (70000−50270)×0.40 = 19730×0.40 = £7,892. Total = £15,432.
Tax on £30,000 = (30000−12570)×0.20 = 17430×0.20 = £3,486. Tax on £40,000 = (40000−12570)×0.20 = 27430×0.20 = £5,486. Difference = £2,000.
More of the £80,000 salary falls into the higher 40% tax band (everything above £50,270), rather than being taxed at 20% like most of the £40,000 salary — so the average rate of tax paid increases as income rises, meaning tax more than doubles even though income exactly doubles.

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