When forecasting it's often useful to know what the compounded rate of change over a given period of time is for a selected variable. As an example, let's say a pharmacy dispenses 50ml of saline in period 1. The following periods it dispenses 57.17ml, 59.25ml, 64.23ml, 65.18ml, and 71.50ml. The actual rates of change for each period are 14.34%, 18.50%, 28.46%, 30.36%, and 43.00% respectively. What formula can you use to calculate a compounded rate of change which will in turn allow you to build a simple linear forecast of how much saline will be dispensed into the near future?

Simply put, the formula is:

((Last Period Data / First Period Data) ^ (1 / Number of Periods)) - 1 

Given the example above, the formula returns a compounded rate of change equaling 7.42%.

The compounded rate of change is calculated as:

(( 71.50 / 50.00 ) ^ ( 1 / 5)) - 1

The result can be proved out as follows:

Finally, a chart visually shows the actual growth (blue line) vs. the compounded growth (red line):

Given the compounded growth rate of 7.42%, the screenshot below shows how the rate is applied to the historical data to estimate two periods into the future (periods six and seven).

The chart has been modified to include the projection periods six and seven:

Please note that this is a very simplistic example that is useful for statistical forecasting only.