(12C) Geometric Mean with Percentage

[Albert Chan]

(07-13-2024 07:08 PM)Thomas Klemm Wrote:  You could just add 100 to the percentages, calculate the geometric mean and subtract 100 from the result.

Or, subtract 100% from each calculation: (1+r1) * (1+r2) - 1 = r1*(1+r2) + r2

Code:

%
LstX
+
+

5 Enter
10 R/S      → 15.5
20 R/S      → 38.6
-50 R/S     → -30.70
20 R/S      → -16.84

Investment return, "average" = -16.84 / 5 = -3.37%
APY = ((1 + -16.84/100)^(1/5)-1) * 100% ≈ -3.62%

Note: Arithmetic mean of returns = (5+10+20-50+20)% / 5 = 1%, yet ROI is negative!