# Probability - question on CAGR formulas

Hey there - wondering if anyone knows the answer to the following:

• when do you use the geometric formula (G=(X1 x X2 x…Xn)^(1/n) to obtain growth rate as opposed to the CAGR forumula (Xn/X1)^(1/(N-1))? - both are related to compound growth rates.

Is the only time you use G= ((1+R1)x (1+R2)…(1+Rn))^(1/n) when one of the rates are negative? i.e. can the above formula (G=(X1x X2…)^1/n) get used for returns as well ?

Cheers.

God I must be freakin tired. Title should be Growth rates…not probability.

X2/X1 -> would give say 0.9 when X2 < X1 if there was a decrease of 10% (1-10% = 0.9) same effect in either formula.

Geometric is for when you have a series of rates, 10%, 12%, 7%, -9% etc. To get the correct annual rate over the four years use the geometric formula. CAGR is for when you have a portfolio of 1m which is worth 1.235m 4 years later. P1/P0^0.25.

I avoid having to make the distinction by always using regular compounding. In Monito’s example, I would treat it like a portfolio and find the final value of one dollar invested: 1.1 * 1.12 * 1.07 * .91, call that X, and the annual growth rate is thus X^(1/4) - 1.

thanks guys