Percentages Advanced
Year 10 (IGCSE) 🔢 Number Repeated percentage change, reverse percentages, compound growth.
💹 Compound Interest
Compound interest earns interest on the accumulated total each period, unlike simple interest which only earns on the original principal.
⚡ Compound Interest Formula
$$A = P\left(1 + \frac{r}{100}\right)^n$$where $P$ = principal, $r$ = annual rate %, $n$ = number of yearsExample: £2000 invested at 3% per year for 4 years: $A = 2000 \times (1.03)^4 \approx £2251.02$
📉 Exponential Decay (Depreciation)
The same multiplier approach models things losing value over time.
⚡ Depreciation Formula
$$A = P\left(1 - \frac{r}{100}\right)^n$$Example: A car worth £15,000 depreciates at 12% per year. After 3 years: $A = 15000 \times (0.88)^3 = 15000 \times 0.6815 \approx £10{,}222$
🔄 Repeated Percentage Change
When different percentage changes are applied in succession, multiply the multipliers together.
Example: A price increases by 20% then decreases by 20%. Combined multiplier: $1.20 \times 0.80 = 0.96$ — the price is now 4% less than the original. A 20% rise followed by a 20% fall never returns to the original value.
The order of percentage changes does not matter for the final result, but the changes never cancel each other out.
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Interactive Demonstration — Percentages Advanced
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💹 Compound Interest Calculator