The formula applied when calculating average growth rates is essentially the formula for compound interest (or a derivation thereof, related to geometric mean).
Explanation:
While the term "compound interest" might initially seem linked only to finance, the underlying principle of growth building on previous growth applies directly to average growth rate calculations. The formula accounts for the cumulative effect of growth over multiple periods. The reference given describes a method that effectively reverses the compounding effect to find the average rate.
Let's break down why it's related to compound interest:
- Compound Growth: Both average growth rates and compound interest deal with a quantity increasing over time, where the increase in each period is based on the value at the end of the previous period.
- Formula Connection: The core calculation involves finding a rate that, when applied repeatedly over a certain number of periods (years, quarters, etc.), results in the observed overall growth. The compound interest formula (or a rearrangement) accomplishes this.
Calculating Average Growth Rate:
The reference provided highlights one method to calculate the average growth rate:
- Divide the present value by the past value. This gives you the total growth factor over the entire period.
- Raise that factor to the power of 1/N (where N is the number of years). This is the key step, and mathematically equivalent to finding the Nth root, effectively "undoing" the compounding over N periods.
- Subtract 1 from the result. This isolates the average growth rate per period as a decimal.
For example, if a company's revenue grew from $100,000 to $161,051 over 5 years, the average growth rate would be:
- 161,051 / 100,000 = 1.61051
-
- 61051 ^ (1/5) = 1.10
-
- 10 - 1 = 0.10 or 10%
Therefore, the average growth rate is 10% per year. This 10% compounded over 5 years equates to the overall growth from $100,000 to $161,051.
Important Note:
This calculation determines the geometric average growth rate. It's important to recognize the distinction from a simple arithmetic average, particularly when growth rates fluctuate significantly. The geometric average provides a more accurate representation of the compounded growth over time.
