Rule 72
There are some useful rules in investing that are good to know and even better to follow. The classic ones are regular, long-term and diversified investing. But there are also more specific rules, such as rule 72 and its use in investing. The Rule of 72 is a quick and useful formula that can be used in two different ways to determine the expected time period for an investment to double or to determine the required rate of return.
In the first case, based on the rate of return, it calculates how long it will take for the value of the investment to double. Alternatively, it can calculate the annual compound rate of return on the investment given how many years it will take for the investment to double. While calculators and spreadsheet programs like Microsoft Excel have functions to accurately calculate the exact time it takes to double your invested money, the Rule of 72 lends itself to quick “off the top of your head” calculations. For this reason, the Rule 72 is often taught to novice investors because it is easy to understand and calculate.
Return on investment
Using the classic Rule of 72, an investor can estimate how long it takes to double their money. We can see that at 7% annual returns, $10,000 will grow to $20,000 in about ten years. While the Rule of 72 serves as a guide to estimating when your money will double, a more accurate way to arrive at this number is by using the logarithmic equation.
At first glance, a 7% return on your investment may not seem that impressive. But what if you heard that your money could double in about 10 years? The graphic below shows how long it takes your money to grow at different annual returns.
Formula to calculate doubling: rule 72 / expected rate of return
The use of rule 72 in practice is shown in the figure below. If the bank offers us a term deposit with an annual return of 2% and we want to calculate how much our invested 1,000 euros will double for, there is no need to use Excel formulas. Off the top of our heads, we can calculate that by dividing 72 (the rule) by 2% (the annual return), the investment will double in value in 36 years. This value is not completely accurate as it would actually double in 35 years. But it is enough to determine the approximate time.
If we were to expect a return of, say, 10%, which is roughly equivalent to the performance of the S&P 500 index over the last 30 years, then according to the Rule of 72, the value of the invested money will double in 7.2 years. In fact, it is in 7.27 years. Similarly, the rule can be used to calculate when the company’s profit will double. If the profit of a prosperous company increases at a rate of 30%, its profit will double in just 2.4 years.
Formula to calculate expected return: rule 72 / Number of years to double
To calculate the expected interest rate, divide the whole number 72 by the number of years it will take to double your investment. The number of years does not have to be a whole number; the formula can handle fractions or parts of a year.
If an investor wants to double the value of his investment within 10 years, based on the formula, he finds that he needs to find an asset that will bring him annual returns of 7.2%. This value came from the calculation of rule 72 divided by the number of years by 10. If an investor wants to double his capital in just 5 years, then his annual return will have to be 14.4%.
Historical return on assets
This formula can therefore also be used to determine a suitable investment asset. If you want to double your deposit within 10 years, you can expect that term deposit, gold and probably not even bonds will be enough for that. Basically, only stock markets achieve similarly high returns.
The table below shows how long it takes for various assets to double based on historical returns between 1928 and 2022. We can see that the 3-month Treasury, often considered the safest asset, has doubled approximately every 21 years. Investors often see this as a place to put cash that is low risk and highly liquid.
Interestingly, real estate assets had a return of 4.4%, doubling roughly every 16 years. Between 1928 and 2022, $100 invested in real estate would be worth $5,121.52. By contrast, the value of $100 invested in the S&P 500, including reinvested dividends, would reach more than $624,000. Data from NYU Stern shows that the S&P 500 has doubled about 10 times since 1949, due to recessions and bull markets, illustrating the power of investing over the long term.
Please note:
– The article is not an investment recommendation
– Historical returns are never a guarantee of future returns
– Investments in the capital markets are always risky