🔢
Number · Foundation & Higher

Percentage change

Percentage change measures how much a quantity has increased or decreased relative to its original value.

🔑

Key facts to remember

  • 1Percentage change = (change ÷ original) × 100.
  • 2A positive result is a percentage increase; negative is a percentage decrease.
  • 3The original value is always the starting value — not the new one.
  • 4Compound interest applies a percentage change repeatedly over multiple periods.
📐

Formulas

Percentage change
((New − Original) ÷ Original) × 100
Compound interest
Final = Principal × (1 + r/100)ⁿ

r = rate, n = number of periods

✍️

Worked examples

Example 1

A jacket costs £80 and is reduced to £60. Find the percentage decrease.

Working

  1. Change = 80 − 60 = 20
  2. Percentage decrease = (20 ÷ 80) × 100
  3. = 0.25 × 100 = 25%
Answer25% decrease
Example 2

£500 is invested for 3 years at 4% compound interest per year. Find the final amount.

Working

  1. Multiplier = 1.04
  2. After 3 years: 500 × 1.04³
  3. 1.04³ = 1.124864
  4. 500 × 1.124864 = £562.43
Answer£562.43
⚠️

Common mistakes

✗Dividing by the new value instead of the original value.
✗Using simple interest instead of compound interest when the question says "compound".
🎯

Exam tips

✓Highlight the word "original" in the question — it's always the denominator.
✓For compound interest, use the multiplier raised to a power rather than calculating year by year.

Ready to test yourself on Percentage change?

Get AI-marked practice questions on exactly this subtopic.

Practice this topic →
← All topicsDashboard

▶️ Watch on YouTube

Free video lessons

Click a topic to search

▶GCSE percentage change▶compound interest GCSE maths▶percentage increase decrease GCSE▶reverse percentage GCSE

Opens YouTube — pick any free GCSE video.