Understanding Percentage Change

Percentage change measures how much a value has increased or decreased relative to its original amount. It is essential for understanding growth rates, price changes, and comparing data over time.

Percentage Increase Formula

Example: Price Increase

A product was $50 and now costs $60:

1. Difference: $60 - $50 = $10
2. Divide by original: $10 ÷ $50 = 0.20
3. Multiply by 100: 0.20 × 100 = 20%
4. Result: 20% increase

Percentage Decrease Formula

Example: Price Decrease

A product was $80 and now costs $60:

1. Difference: $80 - $60 = $20
2. Divide by original: $20 ÷ $80 = 0.25
3. Multiply by 100: 0.25 × 100 = 25%
4. Result: 25% decrease

Important Concept: It's Not Symmetrical!

A 50% increase followed by a 50% decrease does NOT return to the original value!

Example:

• Start: $100
• Increase 50%: $100 × 1.50 = $150
• Decrease 50%: $150 × 0.50 = $75
• You end up with $75, not $100!

Percentage Points vs Percentage Change

These are different concepts:

• Percentage Points: Absolute difference between two percentages
• Percentage Change: Relative change from original to new

Example:

If interest rate goes from 4% to 6%:

• Percentage point increase: 6% - 4% = 2 percentage points
• Percentage increase: (6 - 4) ÷ 4 × 100 = 50% increase

Real-World Applications