What is the Rule of 72?
The rule of 72 is an easy calculation that is used to estimate the time it will take an investor to double their money.
What is the Rule of 72?
The rule of 72 is a quick rule-of-thumb tool to help investors estimate how long it will take an investment to double, assuming a fixed rate of interest or fixed rate of return. Dividing the expected rate of return by 72 yields the estimated number of years that it will take for the investment to double in value.
How Does the Rule of 72 Work?
As an example. The rule of 72 would say that $1 invested with an expected annual rate of return of 8% would take 9 years to double in value. If the rate of return is a fixed rate of interest then the rule of 72 is fairly precise. For investments where the return is variable, such as with stocks, the rule of 72 can be used to estimate the time your investment will take to double in value based on your estimate of the rate of return.
Here is a chart illustrating the time to double your investment at various rates of return using the rule.
| Rate of return | Time for investment to double (in years) |
|---|---|
1% | 72 |
3% | 24 |
6.5% | 11.08 |
9% | 8 |
10% | 7.2 |
12% | 6 |
20% | 3.6 |
40% | 1.8 |
72% | 1 |
100% | 0.72 |
The rule of 72 is an excellent tool to estimate the time it will take an investment to double. The rule tends to be less precise with higher rates of return.
Another way to look at the rule of 72 is that take a time period and go back and estimate the interest rate or rate of return needed on your investment to double your money over that time period. Here are some examples of this.
| Number of years | Rate of return needed to double your investment |
|---|---|
2 | 36% |
5 | 14.4% |
7 | 10.29% |
10 | 7.2% |
20 | 3.6% |
It's important to note that the rule of 72 only works with interest or investment returns that compound over time. In other words, the interest would need to be reinvested in the account or interest bearing investment. In the case of a mutual fund, you would need to assume that all distributions from the fund would be reinvested.
Rule of 72 Formula
The rule of 72 formula is a relatively simple one.
The number of years to double your investment value equals 72 divided by the annual interest rate rote or expected rate of return.
The theory behind this can be explained by an algebraic formula:
$1 x (1+r)n =2
r = the interest rate or expected rate of return
n = the number of years that it will take to double your investment based on the interest rate or the expected rate of return
In this equation you are solving for the number of years that it will take to double the investment given the rate of return assumed.
Those who are interested in delving deeper into the math might look into natural logarithms related to this topic. Natural logarithms will provide a more precise answer than simply dividing 72 by the rate of return.
Along these lines, some experts recommend using 69.3 instead of 72 for a more precise answer.
Rule of 72 examples
Here are a couple of examples to illustrate how the rule of 72 works.
If you have $10,000 invested in a fixed income vehicle that pays an annual interest rate of 4%, then it would take 18 years for the value of the investment to double to $20,000.
In another example, let’s say you have a portfolio of various mutual funds spread among several types of investment types such as large cap stocks, international stocks, small cap stocks and bonds. If you think your pool of mutual funds will return 8% annually, this means that the value of your holdings would double over a 9 year period.
As of December 31, 2021, shares of Apple stock had posted an average annual return of 44.33% over the prior five years. If you felt that Apple shares could maintain this level of growth, an investor would expect to double their investment every 1.62 years. Obviously there is no way to know if an investment with such high returns will continue at this pace into the future.
How to Use the Rule of 72
The rule of 72 is an estimating tool for investors, nothing more or nothing less. It is strictly a numerical exercise.
That said the rule of 72 can be very useful for investors in looking at how their various investments might grow over time. There is nothing particularly magic about doubling your money, but it is an easy benchmark to visualize.
It can also be used as a more general planning tool. Let’s say your goal is to save money for your child’s education and this goal is ten years away. If you have $25,000 already accumulated. In order to double this amount in ten years you would need to earn a return of 7.2%. Using the formula, 72 divided by 7.2 = 10 years.
If you feel that you would need more than $50,000 to achieve your goal, you can plug in different rates of return to see how long it might take to double your money. You can also do this in a sequence.
For example, if you think you can invest and earn an annual return of 16%, this means that you would be doubling your money in 4.5 years. In this case that would give you $50,000 at that point in time. If you felt that you would be comfortable with $100,000 at the end of the ten year time horizon, then you could do another calculation to see what type of return you would need to double your money again within 5.5 years.
In this case, the answer would be 13,09%; 72 divided by 5.5 = 13.09.
If you have ten different holdings in your portfolio, you might estimate a rate of return on each and the time it would take for each holding to double in value. You could then weight these answers based on the relative weighting of each holding as a percentage of the total portfolio to calculate a weighted average time to double the value of your overall portfolio.
Again, it is important to step back and realize that the rule of 72 is just a “quick and dirty” way to estimate the time it will take an investment to double in value. If the investment yields a fixed rate of interest, this calculation will be fairly accurate. In the case of other securities such as stocks and ETFs, it is just an estimate. You will likely want to redo this calculation periodically to see how you are tracking towards doubling your investment.
The rule of 72 is a handy estimating tool, but it is not a substitute for more in-depth analysis in formulating and managing your investment strategy.