Simple interest, percentages over 100% and growth problems

Banks, shops and populations all use percentages. Simple interest stays the same each year; some growth rules repeat a calculation over and over.

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Simple interest

Simple interest is the same amount every year, worked out on the original amount only.
£2400 at 3% for 5 years: 3% of £2400 = £72 a year.
5 × £72 = £360 interest, so the total is £2760.
Compound interest on the same money gives £2782.26, because interest earns interest.

Percentages over 100%

130% of 60 = 1.3 × 60 = 78.
An increase of 150% means multiply by 1 + 1.5 = 2.5.
84 as a percentage of 60: 8460 × 100 = 140%. So 84 is a 40% increase on 60.

Repeating a rule (iteration)

A population starts at 1000. Each year it grows by 20% and then 100 are moved away.
Pn + 1 = 1.2Pn − 100
P1 = 1.2 × 1000 − 100 = 1100
P2 = 1.2 × 1100 − 100 = 1220
Worked example

Find the simple interest on £2400 at 3% per year for 5 years.

  1. One year: 3% of 2400 = 72
  2. 5 years: 5 × 72 = 360

Answer: £360

Key idea

Simple interest: the same amount each year (original × rate × years ÷ 100). An increase of p% multiplies by 1 + p/100, even when p is over 100. For a repeating rule, use each answer to find the next.

Key words
Simple interest
interest = principal × rate × time ÷ 100
Compound interest
Interest paid on the original amount and on interest already added, so the amount grows by the same percentage each period.

All GCSE and International GCSE Mathematics key terms and definitions →

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  1. Find the simple interest on £1200 at 5% per year for 6 years.

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    Answer: 360 £

    5% of 1200 = 60 a year. 6 × 60 = 360.

  2. Work out 150% of 100.

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    Answer: 150

    1.5 × 100 = 150.

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Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.

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