DEFINITION
Growth rate is an indicator that reflects the ratio of the value of a certain indicator of the economy or statistics for the corresponding period of time to its initial value, that is, to the value taken as the basis (base) of the reference.
The growth rate can be measured as a percentage or in relative terms.
The rate of economic growth directly depends on type of economic growth... In the economy, there are two 2 types of economic growth:
- Extensive growth type, in which the increase in production is due to the introduction of a certain, large number of factors (raw materials, fuel, labor, equipment, etc.).
- Intensive type of growth increases production volume by improving quality indicators (qualifications, technologies, achievements of scientific and technological progress). In this type of growth, change occurs through improvements in quality, not quantity.
If there is an intensive type of growth in the economy, then the rates may even decrease slightly when compared with the extensive type. However, this does not indicate a decline in economic development or that it is slowing down.
There are several characteristics of growth types:
- In the case of an extensive type of growth, the economy can maintain proportions, its structural characteristics, while continuing to develop in breadth.
- In the process of an intensive type of growth, the economy can become dynamic due to the expansion of production, as well as due to progressive structural adjustments.
Percentage growth rate formula
In general terms, the percentage growth rate formula is as follows:
Tr = Pnp / Pkp
Here Tr is an indicator of the growth rate,
Rnp - indicator at the beginning of the period,
Ркп - indicator at the end of the period.
In order to get a more visual result, the value obtained is usually multiplied by 100% to express the growth rate formula as a percentage.
Growth rate values
The growth rate reflects the dynamics, by what percentage the statistical indicator of the current period changes (grows) when compared with the value of the previous period.
If you use different values of the formula, then you can see 3 options for the dynamics of values:
1) If the growth rate is more than 100%, then you can observe a positive trend.
2) Growth rate = 100% does not mean any change.
3) A growth rate of less than 100% indicates negative dynamics.
Growth rate and growth rate
Confusion often occurs when defining the concepts of growth rate and growth rate, since their formulas are easily confused.
In order to determine the growth rate from the indicators of the settlement period, the indicator of the base period is subtracted, subsequently this result is divided by the indicator of the base period and multiplied by 100%. As a result, we get the value of the growth rate as a percentage.
In order to avoid confusion in these concepts, it can be noted that the growth rate shows an increase in the indicator itself, that is, how many times it has changed in a certain time interval.
The growth rate shows how much the value of the indicator has grown over this period of time (comparison).
Examples of problem solving
EXAMPLE 1
EXAMPLE 2
| Exercise | For a more accurate understanding of the difference between the rate of growth and growth, calculate the rate of growth and growth by the following indicators: The basic indicator is 140,000 rubles, The reporting indicator is 380,000 rubles. |
| Solution | In order to avoid confusion between the concept of growth and growth, it should be noted that the growth rate is expressed as a percentage of the change in value in the current period when compared with the previous one. For calculations, we will use the following formula: TP = ((P2-P1) / P1) * 100% TP = ((380000-140000) / 140,000) * 100% = 171.43% Percentage growth rate formula: Tr = P 1 / P 2 * 100% Tr = 140,000/380000 * 100% = 36.84% Output. We see that growth rate and growth rate are different indicators. The growth rate characterizes the indicator in dynamics, and the growth rate characterizes the value of the change in the indicator for the selected period. That is, the indicator increased by 36.84%, while it increased by 171.43% compared to the baseline. |
| Answer | Tr = 36.84%, Tr = 171.43% |
The growth rate is one of the dynamic, that is, changing indicators of the economic system. To calculate the indicators of dynamics, you need to establish a baseline level - that is, the one with which all further indicators will be compared.
In economics, the principle of a variable base is often used. This means that each next indicator is compared with the previous one. To understand how to calculate the rate of growth, you need to be able to calculate the baseline.
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Absolute gain
First of all, we need such a concept as absolute growth. Calculating absolute growth is quite simple: to do this, calculate the difference between the latest economic indicators and the previous ones.
For example, if the selected indicator in the reporting period was X rubles, and in the previous reporting period it was Y rubles, then the absolute increase will be X-Y rubles.
The absolute gain can be positive or negative. For this indicator, you can immediately see the increase or decrease of the selected indicator for the selected period.
Rate of increase
The growth rate is indicative of a relative increase. This is a relative value and is calculated as a percentage or fraction, as a growth rate. In order to calculate the growth rate for the selected indicator, the absolute growth for the selected period must be divided by the indicator for the initial period. The resulting value is multiplied by 100 to obtain a percentage.
Consider the above example:
- For the reporting period, the revenue is X rubles, and for the previous period - Y rubles.
- The absolute gain is X-Y.
- The growth rate can now be calculated from the available data: (X-Y) / Y * 100. This indicator can also be positive and negative.
To calculate the growth rate for the entire period, you need to choose an initial, basic level (for example, the year of the company formation). Then the absolute growth is calculated as the difference between the indicators of the last year and the first year. By dividing this difference by the first year, the growth rate for the entire period can be calculated.
The dynamic indicators of the economic system show its efficiency and profitability. One of these indicators is the growth rate, which shows the percentage of growth in indicators.
Mathematical statistics often use the growth rate formula. The growth rate determines the intensity of change (dynamics) of a certain phenomenon.
In order to determine the growth rate, the following indicators are required:
- Initial indicator,
- Basic indicator,
- Several intermediate indicators that are measured at regular intervals.
To calculate the average annual growth rate, a time interval is used that is equal to a month.
The concept of growth rate is used in many areas (economics, finance, statistics, industry, etc.). Growth rate is a statistic that allows analysis:
- Dynamics of a certain process,
- Development speed,
- The intensity of the development of a certain phenomenon, etc.
To calculate the growth rate, the values are compared, which are obtained at selected intervals.
Growth rate formula
In general terms, given the baseline and current indicators, the growth rate formula is as follows:
Tr = Ptek / Pbaz
Here Tr is the growth rate,
Ptek - indicator of the current period,
Pkp - indicator of the base period.
To get a more visual result, the answer is multiplied by 100%, which allows you to express the growth rate as a percentage.
To calculate the average growth rate, it is required to determine the period for which it will be calculated. In most cases, this period is a calendar year or a multiple of it.
Growth rate is a relative concept, since it determines the change in certain values in relation to some initial value. To calculate the average annual growth rate, the initial value is determined as of January 1 of the studied year. The calculation of the average annual growth rate can be carried out in accordance with the values:
- Basic (show the ratio of changes in values in relation to the basic value);
- Chain (show the intensity of changes in the values of adjacent periods or dates).
The general formula for calculating the average annual growth rate is as follows:
Tr cf =
Here n is the number of months (years),
yn is the current indicator,
Features of the formula for the average annual growth rate
The formula for the average annual growth rate uses as a base indicator a numerical value that characterizes the phenomenon under study and is determined at the end of the previous year. Thus, the base value is the value of the indicator as of January 1 of the year for which you want to determine the growth rate.
When calculating the formula for the average annual growth rate by the coefficient, the base indicator is taken as one or 100 (if the calculation is carried out as a percentage). In the process of calculating the baseline growth rate for each month of the year, all indicators at the end of each month should be correlated with the baseline (as of January 1).
When determining chain indicators, the indicator of the previous period is taken as the basic indicator, therefore, when calculating the formula for the average annual growth rate, it is more convenient to calculate using chain indicators.
Average annual growth rate
For the analyzed period, the formula for the average annual growth rate takes a calendar year, that is, the period from January 1 to December 31. This requires data in absolute terms at the end of each month. There should be a total of 13 values (baseline and 12 indicators for each month).
The formula for the average annual growth rate is important, since when calculating it over several years, you can get a result for further analysis and taking into account seasonal fluctuations. The average annual growth rate itself is free from the influence of the seasonality factor.
Examples of problem solving
EXAMPLE 1
EXAMPLE 2
| Exercise | Calculate the average annual growth rate and growth, according to the conditional data of the volume of imports of the state: 2011 - 250 conv. units., |
Many are interested in how to calculate the growth rate for a certain period. When examined in detail, this issue can cause many problems, because it is possible to calculate the growth rate taking into account the base, chain and average indicators with different nuances. We will consider this issue in a simpler context.
Growth rate calculation: formula
In a generalized form, the scheme for calculating the growth rate looks like this: growth rate = data at the end of the period / data at the beginning of the period. For a more visual result, the answer is multiplied by 100%, thus the growth rate will be expressed as a percentage.
Let's consider the application of the growth rate scheme using a specific example. Let's say we need to calculate the growth rate over several years. We have an indicator for 2005 - 240 and we have an indicator for 2013 - 480. In order to calculate the growth rate for these years in percent, we are 480/240 * 100%. Result: 200%. The growth rate was 200%, which means that the indicator we are considering has doubled from 2005 to 2013.
Growth rate is often confused with growth rate, since their formulas are similar, but these indicators are still different. In order to find the growth rate, you need to subtract the basic indicator from the indicator in the billing period, then divide the result by the basic indicator and multiply by 100. The result will be the growth rate in percent. Let's look at the example above. Let's say 240 is the baseline score and 480 is the baseline score. So, (480-240) / 240 * 100% = 100%. The growth rate was 100%.
As you can see, growth rate and growth rate are different indicators. The growth rate shows how the indicator grows, how many times it changes over the period under consideration, and the growth rate shows how much the indicator under consideration increases over a certain period. Each of them is calculated in its own way, so do not confuse them.
Statistical indicators such as growth rates and growth rates are of great importance for analysis, planning indicators in natural sciences, statistics, economics and in other areas.
Their use is widespread in optimizing revenue, wages, turnover, etc.
The meaning of these indicators, their formulas and examples of application will be given below.
Growth rate
It is the ratio of two indicators as a percentage.
It characterizes how many times the new value differs from the previous one (in the basic method) or some constant basic value (the initial value can be taken as it).
Always measured as a percentage.
Rate of increase
This is the percentage by which a value has been changed from the previous or baseline value.
Calculation formulas for the basic and chain method
The basic formulas are shown in the following table:
How to calculate the growth rate as a percentage: calculation examples
To calculate Tp as a percentage, use the formula from the table below.
If the value is calculated from the previous value (chain method), the formula for finding is as follows. 
If the value is calculated in relation to a certain constant value (basic method), then the formula is applied.
For example, let's solve the following problem.
Task.
The table shows Russia's GDP data for 2010 - 2017. in national currency and in US dollars.
| of the year | GDP of Russia | ||
| in billion rubles | in billions of US dollars | ||
| 2010 | 46 309 | 1 487 | |
| 2011 | 59 698 | 1 850 | |
| 2012 | 66 927 | 2 004 | |
| 2013 | 71 017 | 2 097 | |
| 2014 | 77 945 | 1 849 | |
| 2015 | 80 804 | 1 326 | |
| 2016 | 83 898 | 1 267 | |
| 2017 | 88 177 | 1 306 | |
It is required to find the growth rates (in percent) using the basic and chain methods.
Solution .
Let us supplement the table with columns in which we will calculate the required parameter in two ways (in the second method we will take 2010 as the basis).
In national currency, Tr will be as follows:
Difference between growth and growth rates
There is a direct relationship between these values. The difference between them is always 100%. This is reflected in the growth rate formula.
Conclusion
The above formulas are widely used in the daily and business life of the majority of the population. There are online calculators on the Internet that allow you to get a result or check your solutions. Their use allows you to exclude annoying arithmetic errors that entail incorrect answers.
