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 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.
\[500 \times 0.85 \times 1.08 = 459\]
Worked example:
A value of 400 increases by 3% each year for 3 years and then decreases by 5% in the fourth year. Find the final value to 2 decimal places.
Step 1
A 3% increase uses multiplier 1.03. Apply it three times.
Step 2
A 5% decrease uses multiplier 0.95.
\[400 \times 1.03^3 \times 0.95 = 415.23626\]
Answer:
The final value is 415.24 to 2 decimal places.