Compound Percentage Problems

Compound percentage problems involve successive percentage changes — one after another. These are trickier than single percentage changes because of a counter-intuitive result: successive percentage changes do not simply add up. This lesson explains why, shows you the correct method, and covers the common traps.

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Why You Cannot Just Add Percentages

Example: A house worth £200,000 increases by 10% one year and then by 10% the next year.

Intuitive (but wrong): 10% + 10% = 20% increase → £200,000 × 1.20 = £240,000

Correct:

• After Year 1: £200,000 × 1.10 = £220,000
• After Year 2: £220,000 × 1.10 = £242,000

The correct answer (£242,000) is £2,000 more than the intuitive answer (£240,000). This extra £2,000 is the "interest on interest" — the second 10% is applied to £220,000 (which includes Year 1's increase), not the original £200,000.

The Rule: When percentages are applied successively, multiply the multipliers rather than adding the percentages.

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The Multiplier Method

For each percentage change, find the multiplier: