## What Is the Rule of 70?

The rule of 70 is a way of estimating the time it takes to double a number based on its growth rate. It can also be referred to as doubling time. The rule of 70 calculation uses a specified rate of return to determine how many years it'll take for an amount—or a particular investment—to double.

When comparing different investments with different annual compound interest rates, the rule of 70 is commonly used to quickly determine how long it would take for an investment to grow. Although it's only an estimation of the future value of an investment, it can be effective in determining how many years it'll take for an investment to double. The rule of 70 is often used in discussions of population growth, and it can also be used to make estimates about economic growth, usually measured by gross domestic product (GDP).

### Key Takeaways

- The rule of 70 is a way of estimating the time it takes to double a number based on its growth rate.
- The rule of 70 can be effective in determining how many years it will take for an investment to double; it can also be used to make estimates about economic growth, usually measured by gross domestic product (GDP).
- GDP is the total monetary or market value of all the finished goods and services produced within a country's borders in a specific time period.
- Because small differences in annual growth rates result in large differences in the size of economies, the rule of 70 can act as a rule of thumb in order to put different growth rates into perspective.

## The Formula for the Rule of 70

To calculate the rule of 70 for investments, first, obtain the annual rate of return or growth rate on the investment. Next, divide 70 by the annual rate of growth or yield.

$\begin{aligned} &\text{Number of Years to Double} = \frac { 70 }{ \text{ARR} } \\ &\textbf{where:} \\ &\text{ARR} = \text{Annual rate of return, as percentage} \\ \end{aligned}$

## Using the Rule of 70 to Estimate Economic Growth

The rule of 70 can also be used to understand economic growth, usually measured by gross domestic product (GDP). GDP is the total monetary or market value of all the finished goods and services produced within a country's borders in a specific time period. GDP is considered a comprehensive scorecard of a given country’s economic health.

Because small differences in annual growth rates result in large differences in the size of economies, the rule of 70 can act as a rule of thumb in order to put different growth rates into perspective. The rule of 70 approximates how long it will take for the size of an economy to double. The number of years it takes for a country's economy to double in size is equal to 70 divided by the growth rate, in percent.

For example, if an economy grows at 1% per year, it will take 70 / 1 = 70 years for the size of that economy to double. If an economy grows at 2% per year, it will take 70 / 2 = 35 years for the size of that economy to double. If an economy grows at 7% per year, it will take 70 / 7 = 10 years for the size of that economy to double, and so on.

## Rule of 69 vs. Rule of 72 vs. Rule of 70

Some economists refer to the "rule of 69" or the "rule of 72." These are just variations on the rule of 70 concept. The different parameters—69 or 72—reflect different degrees of numerical precision and different assumptions regarding the frequency of compounding.

Specifically, 69 is the most precise parameter for continuous compounding, and 72 is a more accurate parameter for less frequent compounding and modest growth rates. But 70 is an easier number to calculate with, in general.

For example, assume you want to compare the number of years it would take the U.S. GDP to double to the number of years it would take China's GDP to double. Suppose that the United States had a GDP of $21.4 trillion for the current year and a GDP of $20.5 trillion for the previous year. The economic growth rate is 4.3% (($21.4 trillion - $20.5 trillion) / ($20.5 trillion)).

On the other hand, assume China had a GDP of $14.3 trillion for the current year and $13.9 trillion for the previous year. China's economic growth rate is 2.8% (($14.3 trillion - $13.9 trillion) / $13.9 trillion).

It would take approximately 16.28 years (70 / 4.3) years for the U.S. GDP to double. On the other hand, it would take 25 years (70 / 2.8) for China's GDP to double.