What is the Rule of 72? Formula and Calculation
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Summary:
The Rule of 72 formula is a simple equation to calculate how many years it will take for something to double in value. It’s used when calculating things like gross domestic product (GDP), population growth, and investment growth rate. For those looking to see how long their investment or retirement portfolio will take to double in value, the rule of 72 is an easy and accessible way to measure.
The Rule of 72 is a handy tool for investors to quickly estimate how long it will take for an investment to double at a fixed annual rate of interest. To use the rule, simply divide 72 by the annual rate of return. For example, if the annual rate of return is 10%, it would take 7.2 years for an investment to double.
In this article, we’ll discuss the Rule of 72 formula, how you can use the rule in your own investments, and what other rules may come in handy during your calculations.
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Understanding the Rule of 72
The rule of 72 is a simple equation that allows you to estimate the number of years it will take for your investment to double in value. Though the rule can only provide a rough idea, it’s also a valuable tool that investors rely on to estimate increases in value within retirement investments, mutual fund returns, and even investments with exponential growth.
Rule of 72 calculator
This calculator allows you to calculate exactly how many years it will take to double you investment for a given interest rate and compares it to the results you will get using the 72, 70, and 69 rules.
How do you calculate the rule of 72?
You calculate the rule of 72 by dividing the number 72 by the predicted average yearly growth rate of a stock or portfolio, giving you a number of years. This number is the time it will take for an investment to double in value.
Number of years to double = 72/annual growth rate
It’s important to note that the Rule of 72 is most accurate for lower rates of return. As the rates of return increase, the accuracy of the rule decreases. However, the Rule of 72 can also be used to estimate compounding periods using natural logarithms for a more precise estimate.
The time value of money formula can also be used in conjunction with the Rule of 72 to see how long it will take for an investment to double. By stating the future value as 2 and the present value as 1, and simplifying the equation, you can remove the exponent on the right-hand side and take the natural log of each side.
The Rule of 72 is a quick and easy way to get a rough estimate of how long it will take for an investment to double. While it may not be perfectly accurate, it’s a great starting point for investors to make informed decisions.
How can the Rule of 72 help you?
This rule is helpful to many investors, especially those with retirement investments. When planning for retirement, you typically have an age in mind at which you would like to retire. Therefore, you can use this equation to ascertain a rough idea of the annual growth rate and compounded growth you need over time.
- Aggressive growth. Are you hoping to retire within the next ten years? Then you may need a more aggressive portfolio. You can see that if you achieve a growth rate of 12%, you should be able to double it in around six years.
- Safe growth. Maybe you’re risk-averse and you’re planning to retire in a few decades instead. In that case, you can opt for a safe and standard growth rate with the interest calculated at around 5%. At this rate, your portfolio will double in about 15 years.
As you can see from the above examples, you must factor in your investor profile when you compare investments. A person who is 50 needs to gain money quicker, and thus should probably look at a more aggressive portfolio. However, a person who is 25 can invest much more carefully while avoiding risk. Since they have plenty of time for retirement, 15 years to double the value seems more than doable.
If you’re having trouble determining which type of portfolio will suit your needs, you may want to reach out to an investment advisor. Your advisor can point you in the right direction depending on your growth desires.
How do the rules of 69, 70, and 72 differ?
While they all sound similar, the Rule of 72 provides slightly more accurate results (particularly for lower interest rates). In any case, the calculation is the same: divide 69, 70, or 72 by the return of the investment.
Compare the actual time it takes to double an investment with each return rate compared to the results you get with the rule of 69, 70, and 72.
| Return on Investment | Exact number of years | (Rule of 69) | (Rule of 70) | (Rule of 72) |
|---|---|---|---|---|
| 5% | 14.21 | 13.8 | 14 | 14.40 |
| 9% | 8.04 | 7.67 | 7.78 | 8 |
| 12% | 6.12 | 5.75 | 5.83 | 6 |
This table assumes different growth rates for a portfolio at annual growth rates of 5%, 9%, and 12%. Using the rule of 72 you can calculate the number of years it will take for your investment to double in value. As you can see, the rule of 72 is the most accurate of the three (69, 70, and 72)
The Rule of 72 in other contexts
Though useful to calculate doubling time in financial investments, the Rule of 72 can also be used to calculate other forms of growth over time.
- Population growth rate. You can use the same formula listed above to calculate the estimated number of years it would take for a country’s population to double. However, because population growth is subject to multiple outside factors (such as China’s one-family, one-child policy), this rule can only provide an estimate rather than an accurate calculation.
- GDP growth rate. In addition to estimating population growth, the Rule of 72 can be used to approximate the number of years it would take for a country’s GDP to double. For instance, the U.S. had a GDP of $22.99 trillion in 2021 and $20.94 trillion in 2020. That’s a growth rate of about 9.8%. Using the Rule of 72, we can estimate that it would take about 7.35 years to double the U.S. GDP (assuming the growth rate remains the same).
Real growth compared to the Rule of 72
The bottom line is that the Rule of 72, although extremely useful, only provides rough estimates. In this sense, it’s like most models. It does not take into account unforeseen events or knowledge that we do not yet know.
For instance, let’s revisit the U.S. In 1966, the U.S. had a population of approximately 196.6 million. The following year, the U.S.’s population was about 198.7 million. Using the Rule of 72, we can estimate that the growth rate was 2.1%, meaning the U.S. population should approximately double after about 34.3 years.
Except that’s not what happened. In fact, the U.S. population isn’t expected to surpass 400 million people until 2058. Although it’s more of a rough estimate used primarily in the financial sector, the rule of 72 works well to give you an idea of potential growth and what you need to achieve.
Key takeaways
- The Rule of 72 is an equation that allows you to estimate how long it will take for an investment to double with a steady annual growth rate.
- The rules of 69, 70, and 72 are related to the Rule of 72, which are respectively used to calculate compound interest and annual yield.
- The Rule of 72 works best in calculating retirement portfolios, mutual funds, and investments with exponential growth.
- Though the Rule of 72 can also be used to estimate GDP and population growth, it doesn’t take into account unforeseen events or knowledge.
- Despite its other uses, this rule is best used for investment. This is because you can use the historical rate of the stock market for comparison.
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