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Finding the growth factor

If you know the value at two times, you find the growth factor from the ratio between them. After n periods the ratio equals the growth factor raised to n, so you take the n-th root. The percentage is then the growth factor minus 1, multiplied by 100. The method assumes that the percentage has been the same throughout the period. Two points with a changing percentage along the way give only an average growth factor.

Try it yourself

Exponential growth

b = \sqrt[n]{\frac{f(n)}{f(0)}}

growth factor

p = (b - 1) \cdot 100

percent

Symbols

$b$	growth factor per period
$n$	number of periods
$p$	percent	%

Example

From 1000 to 1210 in 2 years: $b = \sqrt{1210/1000} = 1.1$ .

That is $(1.1 - 1) \cdot 100 = 10$ % per year.

The root has the same index as the number of periods.

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Part of Mathematics S1: Exponential models.