Calculating a percentile change in a number is straightforward; calculating the average of a set of numbers is also a familiar task for many people. But what about calculating the average percent change of a number that changes more than once?
For example, what about a value that is initially 1,000 and increases to 1,500 over a five-year period in increments of 100? Intuition might lead you to the following:
The overall percent increase is:
Or in this case,
So the average percent change must be
As these steps show, this is not the case.
Step 1: Calculate the Individual Percent Changes
For the above example, we have
The trick here is recognizing that the final value after a given calculation becomes the initial value for the next calculation.