Compound Interest
Master compound interest for GCSE Maths with structured, exam-style practice. This Foundation and Higher resource covers compound interest calculations and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. Use the multiplier (1 + rate)ⁿ, because interest is earned on interest.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
Compound interest adds interest to the balance, so each year's interest is calculated on a larger amount than the year before. The growth accelerates rather than staying constant.
The efficient method uses a multiplier raised to a power. For 5 percent growth over \(3\) years, multiply by \(1.05^3\). Working year by year gives the same answer but takes far longer and invites rounding errors.
The same structure handles depreciation, where a value falls each year. A 15 percent annual decrease uses a multiplier of \(0.85\), so after \(4\) years the value is the original multiplied by \(0.85^4\).
Revision notes
The multiplier method
Convert the percentage change to a multiplier, then raise it to the power of the number of periods and multiply by the starting amount.
For \(£2000\) at 3 percent for \(5\) years: \(2000 \times 1.03^5 = £2318.55\) to the nearest penny.
Depreciation
A decrease uses a multiplier below \(1\). A 20 percent annual fall uses \(0.8\).
A car worth \(£12\,000\) depreciating at 20 percent per year is worth \(12\,000 \times 0.8^3 = £6144\) after three years.
Finding the number of years
If a question asks how many years until a balance passes a target, calculate year by year until it does, or use trial and improvement with the multiplier.
Round only at the very end. Rounding each year's balance to the penny and carrying it forward introduces errors that grow.
Key points
- Interest is added to the balance each period.
- Use a multiplier raised to the power of the number of periods.
- Growth multiplier is \(1 + \frac{p}{100}\).
- Depreciation multiplier is \(1 - \frac{p}{100}\).
- Compound interest exceeds simple interest over time.
- Round only at the end of the calculation.
Worked examples
Example 1
Find the value of \(£1000\) after \(3\) years at 4 percent compound interest.
Working
Example 2
A car worth \(£15\,000\) depreciates by 10 percent a year. Find its value after \(4\) years.
Working
Example 3
Find the compound interest earned on \(£800\) over \(2\) years at 5 percent.
Working
Common mistakes
Using simple interest by mistake.
Compound interest applies to the growing balance, so 3 years at 5% is 1.05³, not 15% of the original.
Rounding each year and carrying the rounded value forward.
This accumulates error. Use the multiplier to a power and round once at the end.
Giving the total when the interest is asked for.
Subtract the principal from the final amount to get the interest earned.
Using 0.9 for a 10 percent increase.
An increase uses 1.1; 0.9 is a 10 percent decrease.
Exam tips
- Write down the multiplier before doing anything else.
- Use the power key rather than repeated multiplication.
- Subtract the principal when the question asks for interest, not total.
- Round money to the nearest penny only at the final step.
Key terms
- Compound interest
- Interest calculated on the balance including previous interest.
- Depreciation
- A reduction in value over time.
- Multiplier
- The decimal used to apply a percentage change.
- Principal
- The original amount before any interest.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.