## Calculating Growth Rates

The **economic growth rate **can be measured as the annual percentage change of real GDP. The growth rate of real GDP equals:

Because the standard of living depends on **real GDP per person **, which is real GDP divided by the population, we will use the following formulas to calculate and compare standards of living across time or between two different countries.

Growth rate formula for any variable ^{(1) }:

Growth = [(X _{2 }– X _{1 })÷X _{1 }]x100

X _{2 }is the final value and X _{1 }is the initial value of the variable.

Growth (A÷B) is approximately = Growth A − Growth B

Growth (AxB) is approximately = Growth A + Growth B

RGDP per person = RGDP÷Population

Growth rate of RGDP per person = Growth rate of RGDP − Growth rate of population

## The Magic of Sustained Growth

Sustained growth of real GDP per person can transform a poor society into a wealthy one. Even small changes in the rate of growth, when sustained and compounded over long periods of time, make an enormous difference in the standard of living. The slowest rate of GDP per capita growth of 1% per year is similar to what the United States experienced during its weakest years of productivity growth. The 3% per year rate is close to what the U.S. economy experienced during the strong economy of the late 1990s and into the 2000s. Higher rates of per capita growth, such as 5% or 8% per year, represent the experience of rapid growth in economies like Japan, Korea, and China.

An economy growing at a 1% annual rate over 50 years will see its GDP per capita rise by a total of 64%. However, a country growing at a 5% annual rate will see (almost) the same amount of growth over just 10 years. Rapid rates of economic growth can bring profound transformation.

The Rule of 70 demonstrates the magic of economic growth. The Rule of 70 states that the number of years it takes for the level of any variable to double is approximately 70 divided by the annual percentage growth rate of the variable. ^{(1)}

### Self-Check Activity

Let’s practice using The Rule of 70.

**Read the given scenario and questions. Choose the best answer. **^{(1)}

Assume that the U.S. Real GDP is $13 trillion and grows at a 3 percent annual growth rate over the next several decades.

- How long would it take the economy to double in size?
- 13
- 24
- 3
- 34

- How long would it take for the economy to double in size if the growth rate is 2 percent?
- 15
- 25
- 35
- 5