# Growth Rate

If the revenues of a company increase from 1000 to 1100 to 1200 in two years, we can see that the increase if 10% simple growth.

The growth rate can be calculated by finding the increase in two years, (1200 â€“ 1000)/1000 Ã— 100 = 20%, and since it is for two years, we divide by 2 to get an increase of 10%.

This is called the simple rate of growth.

However, when the rate is compounded, as in the case of population or interest or economic growth, then we have to calculate the compounded rate of interest.

In the above example, the value would be 1310 after 2 years.

This called the CAGR â€“ or Compound Annual Growth Rate.

Calculating CAGR is somewhat difficult, especially if the base if not 100.

For instance, what is the CAGR if the sales of a company increase from Rs 76,230 to Rs 1,11,370 in 3 years?

The method to do this is:

76,230(1 + x/100)^{3} = 1,11,370

Anyone can see that it would not be easy to calculate x in this case.

Students should thus learn to arrive at an estimation when such sums are encountered (in data interpretation).

This is how to do it.

First, we see how much increase has occurred. In the above example, it is less that 50%.

So the simple rate of growth in this case would be about 16%.

The actual rate should be less than 16%, since it is compounded.

We can thus venture that the CAGR in this case would be 12-13%.