Compound growth and decay
WJEC Intermediate and Higher candidates apply compound percentage change to financial and biological contexts.
Compound interest
Interest is added at the end of each period, then the next period's interest is calculated on the NEW balance (not the original principal).
Formula: A = P (1 + r/100)ⁿ
where:
- A = final amount,
- P = principal (starting amount),
- r = interest rate per period as a percentage,
- n = number of periods.
✦Worked example
£500 invested at 4% per annum for 3 years.
- A = 500 × 1.04³ = 500 × 1.124864 = £562.43.
- Interest earned = £62.43 (compare to simple interest 3 × £20 = £60).
Compound depreciation (decay)
For depreciation at rate d% per period: A = P × (1 − d/100)ⁿ.
A car worth £18 000 depreciating 12% per year for 4 years: A = 18 000 × 0.88⁴ = 18 000 × 0.5997 = £10 794.81.
Population growth
Same formula. A bacterial culture of 1000 cells growing at 5% per hour for 8 hours: 1000 × 1.05⁸ = 1477.
Comparing simple and compound
Simple interest: I = P × r × n / 100. Linear growth. Compound interest: A = P × (1 + r/100)ⁿ. Exponential growth.
For the same r and n, compound > simple (for n > 1) because of "interest on interest".
Continuous-style problems on Higher
A WJEC Higher question may ask:
- After how many years does an investment first exceed double the original?
Solve P × (1.05)ⁿ > 2P → (1.05)ⁿ > 2. Try n = 14: 1.05¹⁴ = 1.980 (no). n = 15: 1.05¹⁵ = 2.079 (yes). Answer: 15 years.
Iterative processes
WJEC also examines iteration: x_{n+1} = some function of x_n. Use a calculator's ANS button to repeat. Stops when the value stabilises to required d.p.
WJEC exam tip
Carry the multiplier (e.g. 1.04) in your calculator to full precision; rounding it to 1.04 each step will introduce small errors that compound over many years.
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