Percentages
Core formula: Part = Percent × Whole. Rearrange to find any of the three values.
- Finding the part: 30% of 200 = 0.30 × 200 = 60
- Finding the percent: 45 out of 180 = 45/180 = 25%
- Finding the whole: 60 is 30% of what? 60 ÷ 0.30 = 200
Percent change: (New − Old) / Old × 100. Price rises $80 → $100: (100−80)/80 × 100 = 25% increase.
Tax: Final = original × (1 + tax rate). $50 item at 8% tax = 50 × 1.08 = $54.00
Discount: Final = original × (1 − discount rate). 20% off $50 = 50 × 0.80 = $40.00
Critical rule — consecutive percentage changes are NOT additive. A 15% increase then a 15% decrease = 1.15 × 0.85 = 0.9775 → a 2.25% net decrease, not zero.
Simple interest: I = P × r × t (Principal × annual rate × years)
Compound interest: A = P(1 + r/n)^(nt), where n = compounding periods per year. Quarterly → n = 4. Monthly → n = 12.