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Higher Applications of Mathematics

Tax, inflation and financial planning

Planning with tax, inflation and changing costs.

Formula referenceFinance mixed quiz

Formula reference

Check the key Finance formulae and when to use each one.

Mixed revision quiz

Review the whole Finance section with adaptive feedback.

Before you start

  • Calculate percentage increases and decreases.
  • Understand gross pay, net pay and deductions.
  • Use inflation multipliers.
  • Interpret a budget surplus or deficit.

Method chooser

Which method do I use?

Are you finding interest on the original amount only?

Use simple interest.

Is the amount increasing by a percentage repeatedly?

Use compound interest.

Are you finding what future money is worth today?

Use present value.

Are you finding what today's money will be worth later?

Use future value.

Are there regular payments, deposits or withdrawals?

Use a payment timeline.

Are you tracking a loan balance after repayments?

Use a repayment schedule.

Are you comparing insurance policies or risk?

Use expected value and excess comparisons.

Are you working with gross pay, deductions and take-home pay?

Use net pay.

Are you comparing prices over time with inflation?

Use inflation / real value.

Finance lesson

Key idea

  • Financial planning combines income, deductions, tax, inflation, spending and saving. In Higher Applications, you may be asked to justify a decision using calculations and a written conclusion.
  • Gross pay is pay before deductions. Net pay, or take-home pay, is what remains after deductions such as income tax, National Insurance, pension contributions or student loan repayments.
  1. Separate income from deductions and spending.
  2. Calculate net pay before making budget decisions.
  3. Apply inflation using a multiplier such as 1.04 for a 4% rise.
  4. Compare income and spending to find surplus or deficit.
  5. Write a decision or recommendation based on the calculations.

Key formulae

  • Net pay = gross pay − total deductions
  • Percentage change = change / original x 100%
  • Real value after inflation: real value = cash value / (1 + inflation rate)n
  • Budget surplus or deficit = income − spending

Worked examples

Worked example 1

Net pay with deductions

A worker earns £2,850 gross pay in a month. Income tax is £310, National Insurance is £190, and pension contribution is £142.50.

  1. Total deductions = 310 + 190 + 142.50 = 642.50
  2. Net pay = gross pay − deductions
  3. Net pay = 2850 − 642.50 = 2207.50

So: The monthly take-home pay is £2,207.50.

Worked example 2

Inflation and a household budget

A weekly food budget is £86. Inflation on food is 8%. Estimate the new weekly cost and the extra annual cost.

  1. New weekly cost = 86 × 1.08 = 92.88
  2. Weekly increase = 92.88 − 86 = 6.88
  3. Extra annual cost = 6.88 × 52 = 357.76

Final step: The new weekly cost is £92.88. The extra annual cost is about £357.76.

Worked example 3

Annual take-home estimate

A trainee earns £29,400. Estimated annual deductions are income tax £3,180, National Insurance £1,540 and pension £1,176.

  1. Total deductions = 3180 + 1540 + 1176 = 5896
  2. Net annual pay = 29400 − 5896 = 23504
  3. Monthly average = 23504 / 12 = 1958.666..

So: Estimated net pay is £23,504 per year, or about £1,958.67 per month.

Worked example 4

Planning for inflation

A household spends £1,450 per month. Costs are expected to rise by 4.5%.

  1. New monthly spending = 1450 × 1.045 = 1515.25
  2. Monthly increase = 1515.25 − 1450 = 65.25
  3. Annual increase = 65.25 × 12 = 783

Final step: The household should budget about £783 extra per year.

Watch out

  • Confusing gross pay and net pay.
  • Subtracting a percentage without first finding the amount of the deduction.
  • Using the new value instead of the original value in a percentage change calculation.
  • Ignoring inflation when comparing costs over time.

Spreadsheet connection

Spreadsheet connection

Build budget, take-home pay and inflation tables to test financial planning decisions.

Open spreadsheet skill

Next step

Move into practice

Use the method notes to choose the correct financial model, then try varied rates, time periods, tables and decision contexts.

Finance mixed quiz