Lesson 8
Compound Percentages
Understand successive percentage changes.
- intermediate
Formula
Final = Original × (1 + rate₁) × (1 + rate₂) × ...
📚 Compound Percentages
When percentages are applied one after another, they don't simply add up. Each percentage is applied to the new amount.
⚠️ Common Mistake:
A 20% increase followed by a 20% decrease does NOT equal the original!
Frequently Asked Questions
How do successive percentage changes combine?
Multiply the factors: a 20% rise followed by a 10% fall is 1.20 × 0.90 = 1.08, an 8% rise overall, not 10%.
Why doesn't a 50% drop undo a 50% rise?
Because the second change is measured from a bigger base: 100 up 50% is 150, and 150 down 50% is 75. It takes a 33.3% drop to get back to 100.
Practice
Work each one out, then check yourself.
$200 increases by 10%, then decreases by 10%. What's the final amount?
Hint: First: $200 × 1.10 = $220. Then: $220 × 0.90 = ?
Show answer
198
Final Quiz
0/3
Test what you learned. Pick the correct answer for each question.
$100 grows 10% then drops 10%. Final value?
$100 × 1.10 × 0.90 = $99 (not $100).
After two consecutive 50% increases, what happens to $100?
$100 × 1.5 × 1.5 = $225.
$1,000 grows 5% in year 1 and 10% in year 2. Final amount?
$1,000 × 1.05 × 1.10 = $1,155.