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 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.
NumberofYearstoDouble=ARR70where:ARR=Annualrateofreturn,aspercentage
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 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.
Not all investments, such as stocks, grow at a fixed rate, so it can be difficult to know when such an investment will double as it is based on so many factors, e.g. company performance and the economy.
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 of 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.
Example of the Rule of 70
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. The United States had a GDP of $25.46 trillion in 2022 and $23.32 trillion in 2021. The economic growth rate is 9.18% (($25.46 trillion - $23.32 trillion) / ($23.32 trillion)).
On the other hand, China had a GDP of $17.96 trillion in 2022 and $17.82 trillion in 2021. China's economic growth rate is 0.79% (($17.96 trillion - $17.82 trillion) / $17.82 trillion).
It would take approximately 7.63 years (70 / 9.18) for the U.S. GDP to double. On the other hand, it would take 88.6 years (70 / 0.79) for China's GDP to double.
How Is GDP Calculated?
Gross domestic product (GDP) is most commonly calculated as GDP = C + G + I + NX, where C = consumption, also known as consumer spending, G = government spending, I = investment, usually business investment, and NX = net exports.
What Is the GDP of the Richest Country?
The GDP of the richest country, which is the United States, was $25.46 trillion in 2022. It is estimated to be $26.24 trillion in 2023.
Is the Rule of 70 or 72 More Accurate?
Both are fairly accurate measures. Generally, the smaller the number, the better it is suited for more frequent compounding; however, 70 is often simpler to use in calculations.
The Bottom Line
The rule of 70 is used to estimate how long it would take a specific number to double based on its growth rate. While it can be used to determine how long an investment will double given the investment's growth rate, it can also be used to determine how long a country's GDP will double.
It's important to note, however, that GDP growth rates change every year for countries; there is not one static growth rate every year. So the time it takes a country's GDP to double will be either longer or shorter than the calculation made in a given year, depending on how well or poorly a country's economy performs over time.
I'm a financial expert with a deep understanding of investment strategies, economic principles, and financial calculations. My expertise extends to the topic at hand, the rule of 70, and its applications in estimating the time it takes for a number to double based on its growth rate.
The rule of 70 is a powerful tool used to estimate doubling time, commonly applied in the context of investments and economic growth. It allows for a quick assessment of how long it would take for an amount or investment to double based on a specified rate of return or growth rate. This rule is not only applicable to financial investments but also finds relevance in discussions of population growth and economic indicators like gross domestic product (GDP).
GDP, as a fundamental concept, represents the total monetary or market value of all finished goods and services produced within a country's borders in a specific time period. It serves as a comprehensive scorecard for a country's economic health. The rule of 70 becomes particularly handy in approximating the time it will take for an economy to double in size, given its growth rate.
The formula for the rule of 70 in the context of investments involves dividing 70 by the annual rate of return (ARR), expressed as a percentage. This provides a quick estimate of the number of years it will take for the investment to double.
In the realm of economic growth, the rule of 70 is applied similarly. The number of years it takes for a country's GDP to double is calculated by dividing 70 by the growth rate, expressed as a percentage. This facilitates a comparative analysis of different countries or economic scenarios, illustrating how small differences in growth rates can lead to significant disparities in the size of economies.
The article also touches upon variations such as the rule of 69 and the rule of 72, each with specific applications and degrees of numerical precision based on the frequency of compounding.
To illustrate the rule of 70 in action, the article provides an example comparing the time it would take for the U.S. GDP and China's GDP to double based on their respective growth rates. Additionally, it emphasizes the importance of understanding that GDP growth rates change annually for countries, impacting the accuracy of predictions over time.
In summary, the rule of 70 is a valuable tool for estimating doubling time in investments and economic growth. It provides a quick and effective way to put different growth rates into perspective, making it a widely used rule of thumb in the financial and economic domains.
