R4Ratio & ProportionFoundation & Higher

Percentage Change & Growth

When something changes by a percentage again and again — like savings earning interest or a car losing value — you use repeated multipliers. This is compound growth and decay.

40 min Video by Maths Genie AQA GCSE Maths

Compound Interest and DepreciationWatch the walkthrough, then read the notes below.

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What you'll learn

Find a percentage change
Use repeated percentage change
Calculate compound interest
Calculate depreciation

Percentage change

Percentage change $= \frac{change}{original} \times 100$ . A positive answer is an increase; a negative one is a decrease.

% change = \frac{change}{original} \times 100

Always divide by the original.

Compound growth and decay

For repeated change, raise the multiplier to the power of the number of years. £1000 at 5% interest for 3 years is $1000 \times 1.0 5^{3}$ . Depreciation uses a decrease multiplier (e.g. ×0.9 for −10%).

final = start \times (multiplier)^{n}

n = number of times the change happens.

1Multiplier

= 1.05

, applied 3 times.

1000 \times 1.0 5^{3} = £1157.63

Answer£1157.63

Tip — Compound change uses a power; simple change would just multiply once. Read the question carefully.

Remember these

% change = \frac{change}{original} \times 100

Percentage change.

final = start \times r^{n}

Compound growth/decay.

Watch out for these

Dividing the change by the new amount.

Percentage change always divides by the ORIGINAL.

Multiplying by the rate each year separately and adding (simple interest) when compound is asked.

Use the multiplier to the power of the number of years.

Key takeaways

% change = change ÷ original × 100.
Compound change: start × multiplierⁿ.
Depreciation uses a decrease multiplier (e.g. ×0.9).

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