Repeated percentage change means applying percentage multipliers more than once.
If the same percentage change is repeated, use a power of the multiplier; if different percentage changes happen one after another, multiply by each multiplier in order.
Common mistake: Do not just add repeated percentages. Increasing by 20% and then 20% again uses \(1.2^2\), not a single multiplier of \(1.4\).
Worked example:
A value increases by 10% twice. Find the single multiplier.
A 10% increase uses multiplier 1.10.
\[\text{Single multiplier} = 1.10^2\]
\[1.10^2 = 1.21\]
Answer:
The single multiplier is 1.21.
Worked example:
A price of £500 decreases by 15% and then increases by 8%. Find the final price.
Step 1
A 15% decrease uses multiplier 0.85.
Step 2
An 8% increase uses multiplier 1.08.
\[500 \times 0.85 \times 1.08 = 459\]