📚 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!
1
Start: $100
2
+20%: $100 × 1.20 = $120
3
-20%: $120 × 0.80 = $96 (not $100!)
Final = Original × (1 + rate₁) × (1 + rate₂) × ...
🎯 Try It Yourself
Try It Yourself
$200 increases by 10%, then decreases by 10%. What's the final amount?
First: $200 × 1.10 = $220. Then: $220 × 0.90 = ?
📝 Final Quiz
0 / 3
Test what you learned. Pick the correct answer for each question.
1. $100 grows 10% then drops 10%. Final value?
Explanation:
$100 × 1.10 × 0.90 = $99 (not $100).
2. After two consecutive 50% increases, what happens to $100?
Explanation:
$100 × 1.5 × 1.5 = $225.
3. $1,000 grows 5% in year 1 and 10% in year 2. Final amount?
Explanation:
$1,000 × 1.05 × 1.10 = $1,155.
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