The Compounded Annual Growth Rate (CAGR) Formula is:
CAGR= $$CAGR=\left(\frac{Ending\:Value}{Starting\:Value}\right)^{\frac{1}{Number\:of\:Periods}}-1$$
What is the formula if the ending value and the starting value are percentages?
Ex: Starting Period Percentage =0%.
Cumulative Ending Period Percentage at the end of the 13th year= 2794.9%.
I know this evaluates to a CAGR/annual compounded rate of 29.5, but I cannot figure out how to derive this.
Thanks in advance!
Do the start and end percentages mean the starting and ending values are like $(1+0\%)$ and $(1+2794.9\%)$ respectively? That will give $CAGR = 29.5\%$ by your formula.
The general idea seems to be that, imagine there's a base time before the start. In a timeline:
$$\text{Base}\to \text{Start}\ \underbrace{\to \cdots \to\cdots \to}_\text{many periods}\ \text {End}$$
The starting and ending values are both grown from the base value by the given percentages:
$$\begin{align*} \text{Starting value} &= \text{Base value} \cdot (1+\text{Starting percentage})\\ \text{Ending value} &= \text{Base value} \cdot (1+\text{Ending percentage})\\ \end{align*}$$
Then the goal is to find the average growth rate per period from the starting value to the ending value, or $CAGR$:
$$\begin{align*} \text{Ending value} &= \text{Starting value} \cdot (1+CAGR)^{\text{Number of periods}}\\ (1+\text{Ending percentage}) &= (1+\text{Starting percentage})\cdot (1+CAGR)^{\text{Number of periods}} \end{align*}$$