While a expressing change in percent is simple, it can be hard to follow over time. This is especially true if negative percent changes are interspersed with positive percent changes.
final amount =
= (initial amount) * (1 + (first percent change)) * (1 + (second percent change)) * …. * (1 + (nth percent change))
To find the percent that would have given an equivalent change if applied equally over all of the changes:
cumulative percent change =
= ((final amount) / (initial amount)) =
= (1 + (first percent change)) * (1 + (second percent change)) * …. * (1 + (nth percent change))
equivalent percent change =
= ((cumulative percent change) ^ (1/ (number of changes))) - 1
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