How to calculate compound percentage change

[drdoug]

Example: Inflation over time
Supposed that I want calculate the final percent change in a 10 year period.

(year , % Change) --> (1,3) (2,4) (3,7) (4,3) (5,2) (6,5) (7,4) (8,3) (9,4) (10,6)

How should I calculate the final percent inflation without having to calculate one by one?

 

[uart]

100 ( 1.03 * 1.04 * 1.07 ... * 1.06 -1 )

 

[drdoug]

sorry for my laziness but how would you calculate with negative values?

 

[uart]

Each term in the above product is (1 + %change/100).

So for a 3% change (increase) the product term is 1.03, for a 3% decrease you would use 0.97 and so on.

 

[CellCoree]

To calculate the compound percentage change, you would use the formula:

[(1 + % change in year 1) x (1 + % change in year 2) x ... x (1 + % change in year n)] - 1

In this example, you would plug in the values for each year and then subtract 1 from the final result to get the overall compound percentage change over the 10-year period.

[(1 + 0.03) x (1 + 0.04) x (1 + 0.07) x (1 + 0.03) x (1 + 0.02) x (1 + 0.05) x (1 + 0.04) x (1 + 0.03) x (1 + 0.04) x (1 + 0.06)] - 1

= (1.03 x 1.04 x 1.07 x 1.03 x 1.02 x 1.05 x 1.04 x 1.03 x 1.04 x 1.06) - 1

= 1.3494 - 1

= 0.3494 or 34.94%

Therefore, over the 10-year period, there was a compound inflation of 34.94%. Using this formula allows you to calculate the final percent change without having to calculate each year individually.