Percentage Change, Interest, and Growth

Multipliers

• Increase by 15%: multiply by 1.15.
• Decrease by 15%: multiply by 0.85.

Example. $240 increased by 15% = 240 × 1.15 = $276.

Percentage change

Percentage change = (change ÷ original) × 100

A price rises from $50 to $62: change 12, percentage increase = 12/50 × 100 = 24%.

Reverse percentages

After a 20% discount a jacket costs $64. The original price: 64 ÷ 0.8 = $80.

⚠️ Do not take 20% of $64 and add it back; that gives $76.80, which is wrong.

Simple interest

I = P × r × t / 100

$500 at 4% per year for 3 years: I = 500 × 4 × 3/100 = $60.

Compound interest

Amount = P × (1 + r/100)ⁿ

$500 at 4% per year compound for 3 years: 500 × 1.04³ = $562.43 (to the nearest cent).

Exponential growth and decay

• Growth: value × (1 + r/100)ⁿ (population growth).
• Decay: value × (1 − r/100)ⁿ (depreciation).

A car worth $20 000 loses 15% per year. After 2 years: 20 000 × 0.85² = $14 450.

Quick summary

• Use multipliers for increases and decreases.
• Reverse percentage: divide by the multiplier.
• Simple interest adds the same amount each year; compound interest multiplies each year.