# What is the formula for calculating constant percent change?

Sep 13, 2015

For the period from ${t}_{1}$ to ${t}_{2}$ for some state $f \left(t\right)$ with a constant percentage change, that constant percentage change is given by:
color(white)("XX")(f(t_2)/f(t_1)-1)*100%

#### Explanation:

The actual change from ${t}_{1}$ to ${t}_{2}$ is
$\textcolor{w h i t e}{\text{XX}} f \left({t}_{2}\right) - f \left({t}_{1}\right)$

The change as a fraction of its value at ${t}_{1}$ is
$\frac{f \left({t}_{2}\right) - f \left({t}_{1}\right)}{f} \left({t}_{1}\right) \textcolor{w h i t e}{\text{XX")=color(white)("XX}} f \frac{{t}_{2}}{f} \left({t}_{1}\right) - 1$

or,
as a percentage:
color(white)("XX")(f(t_2)/f(t_1)-1)*100%