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
This topic summary covers Knowledge Organiser: Compound Interest and Exponential Change within Compound Interest for GCSE Mathematics. Revise Compound Interest in Ratio & Proportion for GCSE Mathematics with 12 exam-style questions and 4 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 6 of 6 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Compound Interest
Which formula correctly calculates the amount A after compound interest at rate r% per year for n years on principal P?
£2,000 is invested for 4 years. - Account A pays 5% simple interest per year. - Account B pays 4.5% compound interest per year. Which account gives more money after 4 years? Show all working.