Compound interest
Objective. Model repeated percentage growth with multipliers.
- 1. Learn
- 2. Worked example
- 3. Practice
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Learn: the key idea
Compound interest models growth where interest is calculated on the original amount plus any interest already earned, causing the total to increase by a fixed percentage repeatedly over time. The formula uses a multiplier raised to a power: final amount = initial amount × (1 + r/100)ⁿ, where r is the percentage rate and n is the number of time periods. For example, £500 invested at 4% compound interest for 3 years grows to 500 × 1.04³ = 500 × 1.1249 ≈ £562.43. Unlike simple interest, which adds the same fixed amount every period, compound interest grows faster because each period's interest is calculated on an increasingly larger total.
Worked example
£800 is invested at a compound interest rate of 5% per year. Find the total value of the investment after 2 years.
- 1Find the multiplier for 5% growth: 1 + 5/100 = 1.05.
- 2Raise the multiplier to the power of the number of years: 1.05².
- 31.05² = 1.1025.
- 4Multiply by the original amount: 800 × 1.1025 = 882.
Answer: £882
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Practice
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Start practisingCommon mistake. Pupils often multiply the original amount by the percentage rate once and then by the number of years, treating compound interest like simple interest instead of raising the multiplier to a power. Always use (1 + r/100) raised to the power of the number of time periods.
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