Compound annual growth rate

As growth rate is defined as the average relative increase in size per unit time. This is an exponential process is assumed. Instead of the growth rate is usually calculated with the growth constant λ. A growth rate of 23 %, that is 0.23 per year, corresponds to λ = 1.23 / year.

The growth rate is represented by the general formula

Words, where N = T -T0, the number of time units between t0 and t, and A ( t) represents the observed quantity at the time t. The average growth over a period is calculated as the geometric mean.

Annual growth rate ( Compound Annual Growth Rate )

A specific growth rate is the compound annual growth rate (English Compound Annual Growth Rate, CAGR abbreviated ). It represents the average annual growth of a size to be considered dar. to calculate the current value is divided by the initial value. Of the result of the n- th root is taken, wherein n is the number of years, are considered. Thus, the compound annual growth rate represents the average percentage by which to grow the initial value of a time series to hypothetical sequence values ​​for the reference years until the actual value is reached at the end of the reporting period. Actual rashes in subsequent years in the mean effect in this respect not.

In business and economics, the CAGR is a key performance indicator for consideration of investment, market development, sales, etc.

The formula for the CAGR is the same as the growth rate, wherein during CAGR the size N is expressed as a number of years.

Example: A company has a turnover of € 1 million in 2004. In 2006, sales amounted to € 1.21 million. The number of time units N is 2006 - 2004 = 2

The annual growth rate is 10%. Therefore, when the output value multiplied by 1.1 twice, we obtain the final value:

Doubling time

The period in which doubled the population of a country, is called the doubling time. They can be approximated by the growth rate of the country ( given in percent ) calculated as. ( See also 72 rule. )

Specific growth rate in Biotechnology

In exponential growth, the rate of change of cell mass () is at any time proportional to the cell mass. The constant of proportionality is called the specific growth rate.

• Operating performance measure
• Macroeconomic indicator