Problem: You work for a fast growing company. In the first year, they had $970,000.00 in sales. In the fifth year, they had $6,175,000.00 in sales. What was the compounded annual growth rate?
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Strategy: Sales in the fifth year are 6175/970 higher than the first year. The formula for growth is (year 5/year 1) – 100 percent. So, as shown in Fig. 443, the growth rate is 537 percent.
However, a compounded growth rate is a number, x, that will calculate
out like this: Year 1 * (100% + x) *(100% + x) *(100% + x) * (100% + x)= Year 5
This is the same as: Year 1 * (100% + x)^4 = Year 5
So, in order to calculate x, you have to be able to find the fourth root of (Year5/Year1). The formula to find the fourth root is to raise the number to the (1/4) power. Thus, as shown in Fig. 444, the formula to calculate the compounded growth rate is: (Year 5/Year 1)^(1/4)–100% = x
The compounded growth rate is 59 percent.
Summary: Compounded growth rates are common calculations that require you to raise a number to a fractional power.
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