The rule of 70 is a simple method to measure complicated exponential growth without unnecessarily complicated calculations[1]. Investors, who refer to it as doubling time[2], use it to estimate how quickly it would take for an amount (particularly invested money) to double.

The rule of 70 works well when estimating growth that stays constant semiannually or annually[3]. As a result, it can let investors compare different investment vehicles and see how well they would perform in the future.

The rule of 70 is useful not only in investment but also in other areas where there is compounding growth, such as gross domestic product and population. The results of these estimates are valuable when formulating major government policies.

How to Calculate the Rule of 70

To calculate the rule of 70, one simply needs to divide 70 by the annual growth rate or rate of return[4]. This annualized rate indicates the estimated annual yield of an investment and is expressed as a percentage[5].

However, when used in the rule of 70 formula, this rate is always a whole number, not a decimal. For example, a 10 percent annual rate of return (ARR) is expressed in the rule of 70 formula as 10, not 0.10.

The formula is as follows:

Years (to double) = 70 / ARR

For instance, to apply the rule of 70 in a mutual fund with a 3% growth rate, an investor should divide 70 by the mutual fund’s 3% annual rate of return (so 70 divided by 3). The result is 23.3, which means their initial investment will double after 23.3 years or 23 years, 3 months, and 18 days.

In the rule of 70, the constant 70 is derived from the natural logarithm of 2, which is about 0.693, rounded off to 0.70[6].

BY THE NUMBERS: The ideal number in a stocks portfolio of U.S. investors is about 20 to 30 stocks.

Source: Investopedia

Note that the rule of 70 is only an estimate based on a forecasted growth rate. Therefore, once that rate changes, the calculation becomes outdated. When the annual rate of return fluctuates regularly, the investor must also recalculate as needed.

In addition, the rule of 70 applies only to amounts that have compounding growth. An example is an investment with compounding interest, which means interest is also earned on the interest added to the principal. This compounding process allows exponential growth, without which the rule of 70 will become inaccurate.

For example, if the investor does not reinvest the compounded interest and withdraws it, the estimate will fail[7].

Another thing is that the rule of 70 struggles with annual growth rates higher than 10% because it assumes continuous compounding when investments rarely behave this way. As a result, the rule of 70 underestimates doubling time in proportion to how high the annual growth rate is. Therefore, for growth rates beyond 10%, the margin of error becomes too great[4].

In some instances, investors use variants of the rule of 70, the rules of 69 or 72, to predict doubling time. The formula of these two alternatives is the same as that of the rule of 70, but instead of using a constant number of 70, the calculation uses either 69 or 72.

However, there are some differences among these rules, particularly where they are most useful[8].

The rule of 69 delivers a more accurate doubling time estimate when the variable involved is continuously compounding. The rule of 69 is especially useful when interest rates are lower.

The rule of 72, meanwhile, is an alternative when the computation involves annual interest rates. However, it yields a slightly more conservative estimate, making it useful for a more realistic assessment.

Each approach, including the rule of 70 itself, has merits in calculating investments’ doubling time. However, if the variable changes during the lifetime of the calculation, the estimate will be off no matter what constant is used.

• The rule of 70 is a simple formula to quickly estimate the time for an investment to double in value.
• The rule of 70 is particularly helpful for investors comparing the yields of different types of investments in their portfolios, such as stocks and bonds.
• The rule of 70 can also be applied to other areas where there is compounding growth, such as estimating the doubling time of GDP and population.

1. Go Cardless. (n.d.) Understanding the Rule of 70. gocardless.com. Retrieved from https://gocardless.com/en-us/guides/posts/understanding-the-rule-of-70/
2. Evans, K. (n.d.) What Is the Rule of 70 and How Do Investors Use It? Go Banking Rates. Retrieved from https://www.gobankingrates.com/investing/strategy/rule-of-70/
3. Master Class. (2021.) How to Calculate the Rule of 70. Retrieved from https://www.masterclass.com/articles/rule-of-70-explained
4. Dibartolomeo, M. (2021.) What Is the Rule of 70? The Kelly Financial Group. Retrieved from https://www.thekelleyfinancialgroup.com/post/the-rule-of-70
5. Twin, A. (2021.) Annualized Rate of Return. Investopedia. Retrieved from https://www.investopedia.com/terms/a/annualized-rate.asp
6. Purplemath. (n.d.) The Common and Natural Logarithms. Retrieved from https://www.purplemath.com/modules/logs3.htm
7. Aldrich, E. (2021.) The Rule of 72 Is a Quick and Simple Formula to Estimate When Your Investments Will Double. Insider. Retrieved from https://www.businessinsider.com/rule-of-72
8. Demarco, J. (2021.) What Is Rule of 70? The Balance. Retrieved from https://www.thebalance.com/what-is-the-rule-of-70-5198230