Ratio & ProportionTopic Summary
Knowledge Organiser: Compound Interest and Exponential Change
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.
Topic position
Section 6 of 6
Practice
12 questions
Recall
4 flashcards
Knowledge Organiser: Compound Interest and Exponential Change
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