How to Calculate an Annual Percentage Growth Rate

How to Calculate an Annual Percentage Growth Rate.

Annual percentage growth rates are useful when considering investment opportunities. Municipalities, schools and other groups also use the annual growth rate of populations to predict needs for buildings, services, etc. As important and useful as these statistics are, it is not difficult to calculate annual percentage growth rates.

Method 1 Calculating Growth Over One Year.
1. Get the starting value. To calculate the growth rate, you're going to need the starting value. The starting value is the population, revenue, or whatever metric you're considering at the beginning of the year.
For example, if a village started the year with a population of 150, then the starting value is 150.
2. Get the final value. To calculate the growth, you'll not only need the starting value, you'll also need the final value. That value is the population, revenue, or whatever metric you're considering at the end of the year.
For example, if a village ended the year with a population of 275, then the final value is 275.
3. Calculate the growth rate over one year. The growth is calculated with the following formula: Growth Percentage Over One Year = {\displaystyle {\frac {FinalValue-StartValue}{StartValue}}*100}{\frac  {FinalValue-StartValue}{StartValue}}*100.
Example Problem. A village grows from 150 people at the start of the year to 275 people at the end of the year. Calculate its growth percentage this year as follows.
Growth Percentage {\displaystyle ={\frac {275-150}{150}}*100}={\frac  {275-150}{150}}*100
{\displaystyle ={\frac {125}{150}}*100}={\frac  {125}{150}}*100
≈ {\displaystyle 0.8333*100}0.8333*100
= {\displaystyle 83.33\%}83.33\%.

Method 2 Calculating Annual Growth over Multiple Years.
1. Get the starting value. To calculate the growth rate, you're going to need the starting value. The starting value is the population, revenue, or whatever metric you're considering at the beginning of the period.
For example, if the revenue of a company is $10,000 at the beginning of the period, then the starting value is 10,000.
2. Get the final value. To calculate the annual growth, you'll not only need the starting value, you'll also need the final value. That value is the population, revenue, or whatever metric you're considering at the end of the period.
For example, if the revenue of a company is $65,000 at the period, then the final value is 65,000.
3. Determine the number of years. Since you're measuring the growth rate for a series of years, you'll need to know the number of years during the period.
For example, if you want to measure the annual revenue growth of a company between 2011 and 2015, then the number of years is 2015 - 2011 or 4.
4. Calculate the annual growth rate. The formula for calculating the annual growth rate is Growth Percentage Over One Year {\displaystyle =(({\frac {f}{s}})^{\frac {1}{y}}-1)*100}=(({\frac  {f}{s}})^{{{\frac  {1}{y}}}}-1)*100 where f is the final value, s is the starting value, and y is the number of years.
Example Problem: A company earned $10,000 in 2011. That same company earned $65,000 four years later in 2015. What's the annual growth rate?
Enter the values above into the growth rate formula to find the answer:
Annual Growth Rate {\displaystyle =(({\frac {65000}{10000}})^{\frac {1}{4}}-1)*100}=(({\frac  {65000}{10000}})^{{{\frac  {1}{4}}}}-1)*100
{\displaystyle =(6.5^{\frac {1}{4}}-1)*100}=(6.5^{{{\frac  {1}{4}}}}-1)*100
≈ {\displaystyle (1.5967-1)*100}(1.5967-1)*100
= 59.67% annual growth.
Note — raising a value a to the {\displaystyle {\frac {1}{b}}}{\frac  {1}{b}} exponent is equivalent to taking the bth root of a. You will likely need a calculator with an "{\displaystyle n{\sqrt {x}}}n{\sqrt  {x}}" button, or a good online calculator.

FAQ.

Question : Say that my company projects the next three years' revenue, 2016 with $300,000, 2017 with $350,000, and 2018 with $320,000. What is the percentage increase or decrease in revenue?
Answer :  2017 compared to 2016 an increase of 17%; 2018 compared to 2017 a decrease of 8.6%
Question : If my house value doubled in 12 years, what was the percentage rate growth each year?
Answer : The compound annual rate of growth is 6%. Calculate that by using the "Rule of 72": Divide 72 by the number of years it takes an investment to double in value, and that is the compound rate of growth over the period of time applied.
Question : I started with 125 members in a group. 3 years later, we now have 700 members in the group, what is our growth percentage in 3 years?
Answer :  Your growth rate has been 460% over 3 years.
Question : How can I calculate the percentage of population change in the decade?
Answer :  Take the population at end of the decade. Subtract it from population at beginning of decade. That is the total population change. Convert to a percentage. Divide the population change by the population at beginning of the decade. Multiply by 100.
Question : What is the annual increase of 3% of 2600?
Answer : 3% of 2600 is (.03)(2,600) = 78.
Question : What does the upside "v" mean?
Answer : To the power of. It's a common way to write out powers when a number can't be formatted as a superscript. 2^2 means 2 squared, for example.
Question : How did it go from (6.5^1/4-1) * 100 to (1.5967 -1) * 100? You didn't explain how you got rid of the "1/4" or how you ended up with 1.5967? Can you please clarify?
Answer :  (6.5^1/4-1)*100 would be represented as (6.5^0.25-1)*100. This is how you get to (1.5967-1)*100.
Question : The population of my town is 100,000. How many years will it take for the population to double at an average annual growth of 0.5 %?
Answer : Using the formula for "doubling time" (t = 70 / r, where t is time in years, and r is the annual rate of growth), the doubling time in this case is 70 / 0.5 = 140 years.