How to Solve Compound Percentage Questions
In IGCSE Maths, compound percentages are used when a percentage increase or decrease happens repeatedly over time. Each step updates the amount first, then the next percentage is applied, so the change builds on itself. You'll see this in compound interest, depreciation and multi step percentage problems. This page shows the year by year method and the formula method with exam style examples.
Two reliable approaches
Year-by-year method
Apply the percentage once per year and carry the result forward. Each step acts on the most recent amount, not the original.
💡 Example 1A: Increase (year-by-year)
£\(1000\) grows by \(5\%\) each year for \(4\) years.
\[ \begin{aligned} \text{Year 0 (principal)} &= 1000 \\ \text{Year 1} &= 1000 \times 1.05 \\ \text{Year 2} &= \text{Year 1} \times 1.05 \\ \text{Year 3} &= \text{Year 2} \times 1.05 \\ \text{Year 4} &= \text{Year 3} \times 1.05 \\ \text{Year 4} &\approx 1215.51 \end{aligned} \]💡 Example 2A: Decrease (year-by-year)
£\(1200\) depreciates by \(12\%\) per year for \(3\) years.
\[ \begin{aligned} \text{Year 0 (principal)} &= 1200 \\ \text{Year 1} &= 1200 \times 0.88 \\ \text{Year 2} &= \text{Year 1} \times 0.88 \\ \text{Year 3} &= \text{Year 2} \times 0.88 \\ \text{Year 3} &\approx 817.77 \end{aligned} \]Formula method
Jump straight to the final amount with one calculation:
\[A = P\left(1 \pm \frac{r}{100}\right)^{n}\]
\(P\) = initial amount, \(r\) = percentage rate per year, \(n\) = number of years, \(A\) = final amount.
💡 Example 1B: Increase (formula)
£\(1000\) grows by \(5\%\) each year for \(4\) years.
\[ \begin{aligned} A &= P\left(1+\frac{r}{100}\right)^{n} \\ A &= 1000\left(1+\frac{5}{100}\right)^{4} \\ A &= 1000\,(1.05)^{4} \\ A &\approx 1215.51 \end{aligned} \]💡 Example 2B: Decrease (formula)
£\(1200\) depreciates by \(12\%\) per year for \(3\) years.
\[ \begin{aligned} A &= P\left(1-\frac{r}{100}\right)^{n} \\ A &= 1200\left(1-\frac{12}{100}\right)^{3} \\ A &= 1200\,(0.88)^{3} \\ A &\approx 817.77 \end{aligned} \]Compound interest in real life
Compound Interest Calculator (quick demo)
Educational tool for IGCSE maths only. Not for financial planning.
Start early, stay consistent. Orange: your principal compounding with no contributions. Green: add monthly savings with no interest on them. Blue: those same contributions also compounding. The gap between green and blue is what compound interest earns on your monthly savings.
Showing: £1,000 at 5% p.a. over 4 years (annual, principal only)
Orange: principal compounding, no contributions. Green dashed: principal + flat monthly savings (no interest on contributions). Blue dashed: principal + contributions also compounding.
🔑 Key points
- Compound change acts on the latest amount each step, not the original.
- Formula: \(A=P\!\left(1\pm \tfrac{r}{100}\right)^n\) for whole-year compounding in exam questions.
- Mixed rates multiply in order; successive discounts multiply together (they do not add).
- Money answers are usually rounded to the nearest penny; show one equation per line in working.
With practice, compound percentages become routine: pick year-by-year or jump straight to the answer with the formula. These skills appear frequently in IGCSE exam questions.
Ready to test yourself? Try the practice rooms below.
Next topic: Inverse Percentages →