Compound Interest, Knowledge Organiser

Key Terms

• Compound interest: Interest calculated on the original amount AND on previously earned interest
• Exponential growth: Repeated percentage increase over time (multiplier > 1)
• Exponential decay: Repeated percentage decrease over time (multiplier < 1)
• Multiplier: The number raised to a power: (1 + r) for growth, (1 - r) for decay
• Depreciation: A repeated percentage decrease in value (e.g. a car losing value each year)

Must-Know Facts

• Compound interest applies the percentage to a growing total, not a fixed original
• Growth formula: y = a × (1 + r)ⁿ
• Decay formula: y = a × (1 - r)ⁿ
• r is the rate as a decimal (e.g. 5% → r = 0.05)
• n is the number of time periods (years, hours, etc.)
• Use the power (xⁿ) button on your calculator

Key Formulas

• Growth: y = a × (1 + r)ⁿ
• Decay: y = a × (1 - r)ⁿ
• Compound interest: A = P × (1 + r)ⁿ
• Multiplier for growth: 1 + (% ÷ 100)
• Multiplier for decay: 1 - (% ÷ 100)

Common Mistakes

• Simple vs compound: Simple interest gives the same amount each year; compound recalculates on the growing total
• Rate as percentage: r must be a decimal: 5% per year means r = 0.05, so multiplier is 1.05
• n is number of periods: If investing for 3 years, use n = 3, not n = 4
• Decay multiplier: 10% depreciation uses 0.9, NOT 1.1
• Rounding mid-calculation: Keep full calculator accuracy and only round the final answer

Worked Examples

A colony of 500 bacteria grows by 20% each hour. How many after 5 hours? Step 1 Identify type and multiplier Growth, so multiplier = 1 + 0.20 = 1.2 Step 2 Write formula y = 500 × 1.2⁵ Step 3 Calculate y = 500 × 2.48832 = 1244 bacteria (to nearest whole)

Worked Examples

A car worth £12,000 depreciates by 15% per year. What is it worth after 3 years? Step 1 Identify type and multiplier Decay (depreciation), so multiplier = 1 - 0.15 = 0.85 Step 2 Calculate y = 12000 × 0.85³ = 12000 × 0.614125 = £7369.50