Simple & Compound Interest, Growth & DecayEdexcel GCSE Maths: Revision notes
Section 1
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal every period, so it grows by the same amount each year.
Compound interest is calculated on the running total (principal plus interest already earned), so it grows by an increasing amount each year — this is the standard model for savings, loans, and other growth/decay contexts.
| Simple interest | Compound interest | |
|---|---|---|
| Calculated on | Original principal only | Running total (principal + interest so far) |
| Growth pattern | Same amount each year | Increasing amount each year |
Section 2
How do we use the compound growth/decay formula?
The compound growth/decay formula is:
A = P(1 ± r/100)ⁿ
where P is the original amount (principal), r is the percentage rate, n is the number of time periods, + is used for growth (e.g. compound interest, appreciation) and − is used for decay (e.g. depreciation).
- £2000 invested at 4% compound interest for 3 years: A = 2000 × 1.04³ = £2249.73 (to 2 d.p.)
- A car worth £8000 depreciates by 15% per year for 2 years: A = 8000 × 0.85² = £5780
Always identify whether the context is growth (use +) or decay (use −) before substituting into the formula — this is the most common source of errors.
Section 3
How do we work with general iterative processes for growth and decay?
Some growth and decay problems build up year by year rather than using the formula directly — this is an iterative process, where each year's result becomes the starting value for the next year's calculation.
This approach is useful when the rate changes between periods, or when a question asks for the value after each individual year (e.g. a table showing year 1, year 2, year 3).
- Year 1: £5000 × 1.03 = £5150
- Year 2: £5150 × 1.03 = £5304.50
- This matches 5000 × 1.03² = £5304.50, confirming the iterative and formula methods agree
Section 4
How do we solve problems involving repeated proportional change?
Repeated proportional change describes any situation where a quantity changes by the same percentage multiple times in a row — this is exactly what the compound formula models, but it can appear in varied real-life contexts: population growth, radioactive decay, bacteria multiplying, investment growth, or price inflation.
To solve: identify P (starting amount), r (rate of change per period) and n (number of periods), decide growth or decay, then substitute into A = P(1 ± r/100)ⁿ.
Some questions work backwards — given the final amount, find the rate or number of years using trial and improvement or logarithm-free estimation methods appropriate at GCSE level.
A population of bacteria doubles (grows by 100%) every hour, starting at 50. After 4 hours: 50 × 2⁴ = 800
Must Know
- Simple interest is calculated on the original principal only; compound interest is calculated on the running total
- Compound growth/decay formula: A = P(1 ± r/100)ⁿ
- Use + for growth (interest, appreciation), − for decay (depreciation)
- n represents the number of time periods, not always years
- An iterative, year-by-year calculation should give the same answer as the compound formula
- Repeated proportional change situations (population, radioactive decay, investments) all use the same compound formula structure
That's the notes covered.
Carry on to the next subtopic.