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Higher Applications of Mathematics

Savings and pensions

Long-term saving, growth and retirement planning.

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 percentages of salary.
  • Use compound growth over many years.
  • Understand monthly and annual contribution amounts.
  • Know that inflation reduces real purchasing power.

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

  • Savings and pensions are long-term finance models. Regular contributions, employer contributions, investment growth and inflation all affect the real value of the final amount.
  • Pension questions often compare money values across many years, so small percentage changes can have large effects. Inflation reduces purchasing power, even if the cash amount rises.
  1. Calculate employee and employer contributions separately.
  2. Convert monthly contributions to annual amounts where needed.
  3. Apply growth to existing savings or pension pots.
  4. Adjust future values for inflation if the question asks for real value.
  5. Use a written conclusion because pension planning includes uncertainty.

Key formulae

  • Future value: FV = PV(1 + r)n
  • Real value after inflation: real value = cash value / (1 + inflation rate)n
  • Total monthly pension contribution = employee contribution + employer contribution

Worked examples

Worked example 1

Employer pension contributions

A worker earns £32,000. They pay 5% into a pension and their employer pays 3%. Find the total annual contribution.

  1. Employee contribution = 0.05 × 32000 = 1600
  2. Employer contribution = 0.03 × 32000 = 960
  3. Total contribution = 1600 + 960 = 2560

So: The total annual pension contribution is £2,560.

Worked example 2

Inflation and purchasing power

A pension pot is expected to be £180,000 in 20 years. Inflation is assumed to be 2.5% per year. Find its value in today's money.

  1. Use real value = cash value / (1 + inflation rate)n.
  2. Real value = 180000 / 1.02520
  3. Real value = 180000 / 1.638616... = 109848.81..

Final step: The pension pot has purchasing power of about £109,848.81 in today's money.

Worked example 3

Monthly contributions

A worker pays £180 per month into a pension and their employer pays £120 per month. Find the total paid in over 15 years before growth.

  1. Monthly total = 180 + 120 = 300
  2. Annual total = 300 × 12 = 3600
  3. Over 15 years: 3600 × 15 = 54000

So: The total contribution before investment growth is £54,000.

Worked example 4

Savings target with inflation

A saver expects to need £30,000 in today's money in 12 years. Inflation is 2.4%. Find the cash target in 12 years.

  1. Inflate today's amount forwards.
  2. Future cash target = 30000(1.024)12
  3. Future cash target = 30000 × 1.3290..

Final step: The saver should target about £39,870.42.

Watch out

  • Ignoring employer contributions when finding total pension saving.
  • Assuming a future cash amount has the same buying power as today.
  • Mixing monthly and annual contributions.
  • Forgetting that investment growth is uncertain, unlike a fixed savings rate.

Spreadsheet connection

Spreadsheet connection

Model long-term contributions, employer contributions, growth and inflation assumptions.

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