Exponential Growth
Each period builds on the previous total, not the original. This is compounding — the core of CAGR.
Practice This ConceptUnderstanding Exponential Growth
In linear growth, you add the same amount each period. In exponential growth, you add a percentage of the CURRENT total. After year 1 at 10%, 100 becomes 110. After year 2: 110 x 1.10 = 121, not 120. This compound vs simple difference is exactly what EPSO tests.
Formula
$V_t = V_0 \times (1 + r)^t$
Key Rules
- Compound growth builds on itself each year
- 10% for 3 years = 1.10^3 = 1.331 (33.1% total, not 30%)
- Compound rate is always LOWER than total / years
- Small rates over many years compound significantly
Examples in Action
1
100 x 1.10^3
=
133.1
10% compound over 3 years (not 130)
2
(658/498)^(1/4) - 1
=
7.2%
CAGR of Poland GDP over 4 years
3
1000 x 1.05^10
=
1628.9
5% over 10 years = 62.9% total, not 50%
Common Errors
- Using total% / years instead of compound formula
- Not recognizing "annual growth rate" implies compounding
- Confusing growth multiplier (1.05) with growth rate (5%)
Pro Tip
If a question mentions growth over multiple years and asks for annual rate, it is ALWAYS compound. Simple division is always a distractor.