I was recently familiarizing myself with CAGR formulae and spotted that several sources interpret the formula in different ways.
METHOD ONE: from Wikipedia
$V_0$=9000 (2004), $V_n$=13000 (2007)
$ \mathrm {CAGR} (t_{0},t_{n})=\left({\frac {V(t_{n})}{V(t_{0})}}\right)^{\frac {1}{t_{n}-t_{0}}}-1$
Which gives us the CAGR value to be 13%.
${\rm CAGR}(0,3) = \left( \frac{13000}{9000} \right)^\frac{1}{3} - 1 = 0.13 = 13\%$
METHOD TWO: Extend Office
However, other sources appear to count the number of years differently, namely using the (N-1) notation, such as here:(https://www.extendoffice.com/documents/excel/2596-excel-average-compound-growth-rate.html):
Where instead of $t_n -t_0$ the author is counting all the periods and subtracting one. In this particular example, the date range of 2011-2020 is counted as 9 years (the distance between $t_n$ and $t_0$).
For now, both methods of calculating years line up, which doesn't affect the answers.
METHOD THREE: CAGRCALCULATOR
What get's confusing is when some sources appear to count the total number of years including the original year, such as here (https://cagrcalculator.net/formula-for-cagr-calculation/), where between 2008 and 2016 is counted as 9 years, where the prior formulae would return 8.
Putting aside the gotchas of calculating CAGR and treating it as the definitive growth metric, which one of these is correct?