• Smart Cash
• Performance
• Get Started

How does the Rule of 72 work?

Why is the Rule of 72 used?

Who invented the Rule of 72?

Why is it called the Rule of 72?

LearnRate of ReturnWhat Is the Rule of 72?

# What Is the Rule of 72?

Jul 27, 2022

·

The Rule of 72 is an easy, concise equation that calculates the amount of time your investment will need to increase its value twofold.

The Rule of 72 is an easy, concise equation that calculates the amount of time your investment will need to increase its value twofold.

It's a reasonably accurate way to manually gauge an investment's growth rate or rate of return, which is an investment's net gain or loss over a specific period of time, without having to rely on elaborate software, complicated algebra, or other logarithmic calculating tools.

The Rule of 72 yields the most accurate results when interest rates are low, usually between 6 and 10 percent. The formula gives the most precise answers when the rate of return is 8 percent.

## How does the Rule of 72 work?

Using the Rule of 72 is simple. Essentially all you need is one piece of information: the expected annual growth rate of your investment, which is also sometimes referred to as "rate of return" or "RoR."

Here's how the equation works: divide the number 72 by the expected annual growth rate. This determines the number of years it will take for your investment to double.

For example, if you invest \$1,000 and the growth rate is 8 percent, all you have to do is divide 72 by eight, which is nine. That's to say, it will take approximately nine years for your \$1,000 investment to become \$2,000.

Let's say you invest \$60,000 in a friend's doggy daycare startup or a loved one's new cafe. If the expected annual growth rate of your investment is 10 percent – which is interest that the borrower pays the lender – using the Rule of 72 lets you know that it will take slightly more than seven years – 7.2 years, precisely – for your \$60,000 investment to become \$120,000. Doing the math, 72 divided by 10 is 7.2.

If the expected annual rate of return is 2 percent, however, it would take approximately 36 years for your investment to double.

Simply put, the higher the annual growth rate of the investment, the quicker the profit.

That may seem pretty obvious, even if you're no math wiz. A steeper rate of return equals a faster return. What's particularly useful about the Rule of 72 is that it allows you to determine just how much time it will take for your investment to come full circle. That, in turn, helps you to decide whether a particular investment opportunity is savvy or a financial Pandora's box that's better of which to steer clear.

## Why is the Rule of 72 used?

Essentially, the Rule of 72 can apply to anything that grows at a compounded interest rate or a rate that is based on the initial amount of investment.

In the financial world, experts use the Rule of 72 to determine the monetary return on anything that grows exponentially, such as a loan. Economists also use it to anticipate the growth rate of a country's gross domestic product or its national currency's inflation.

When it comes to lending capital, the Rule of 72 helps assess the overall impact that annual fees will have on your investment's growth over the life of the loan.

The Rule of 72 also serves a purpose beyond banking and investing. Social scientists use it to determine population growth rates, whether locally, nationally, internationally, or globally.

For example, if a city's population is 1 million residents and it has an annual growth rate of 7 percent, using the Rule of 72 you can calculate that it will take approximately 10.28 years for the population to reach 2 million. That is, as long as the annual growth rate remains the same. If it rises or falls, the time it takes for the population to grow to 2 million could be shorter or longer.

## Who invented the Rule of 72?

The concept of interest, in general, has been around since Mesopotamian times – 6,000-7,000 years ago – when humans began to develop more complex ways of managing newfound agricultural-based economic systems by way of land and money loans.

As far as the first known mention of the Rule of 72 goes, Italian mathematician Luca Pacioli explained the theory in his 1494 book "Summary of Arithmetic, Geometry, Proportions, and Proportionality."

Thanks to Pacioli's reference, historians and mathematicians alike generally consider him the father of the Rule of 72.

## Why is it called the Rule of 72?

So, what's so special about the number 72 when it comes to figuring out how long it will take to double your money invested? It's no magic. It's just simple math.

The actual formula to determine the precise amount of time it would take for an investment to double is a bit more complicated, to say the least: ln(2) / ln(1 + (interest rate/100)), with "ln" representing natural log value as it would on a calculator.

To gauge an even more precise estimate, investors will sometimes stray from the Rule of 72 by substituting a slightly different number as the dividend, such as 70 or 69.

This is because the exact number to find the most accurate return time on your investment is 69.3, not 72. But since 69.3 isn't exactly the easiest number to divide by without the help of a calculator, you can substitute it for another nearby number which is. Many more numbers yield even results when divided into, let's say, 70: the numbers 1, 2, 5, 7, and 10.

In fact, if you enter ln(2) on a calculator, the result is .69314718056. Or, after moving the decimal two spots to the right, 69.3.

Investors use the number 72 because several numbers divide evenly with it, including the numbers 1, 2, 3, 4, 6, 8, 9, and 12. This allows for a quick, easy, and reasonably accurate assessment of the amount of time it will take an investment to double with a wide range of growth rate percentages.

Given that it's simple, easy, and reliable, it's no surprise why the Rule of 72 is such a go-to lifesaver in the fast-paced world of finance.

Whether you're looking to invest a little or a lot, knowing how to apply the Rule of 72 will help you anticipate exactly how long it will take until you see your profits come rolling in.

At Titan, we are value investors: we aim to manage our portfolios with a steady focus on fundamentals and an eye on massive long-term growth potential. Investing with Titan is easy, transparent, and effective.

Get started today.

Disclosures

Certain information contained in here has been obtained from third-party sources. While taken from sources believed to be reliable, Titan has not independently verified such information and makes no representations about the accuracy of the information or its appropriateness for a given situation. In addition, this content may include third-party advertisements; Titan has not reviewed such advertisements and does not endorse any advertising content contained therein.

This content is provided for informational purposes only, and should not be relied upon as legal, business, investment, or tax advice. You should consult your own advisers as to those matters. References to any securities or digital assets are for illustrative purposes only and do not constitute an investment recommendation or offer to provide investment advisory services. Furthermore, this content is not directed at nor intended for use by any investors or prospective investors, and may not under any circumstances be relied upon when making a decision to invest in any strategy managed by Titan. Any investments referred to, or described are not representative of all investments in strategies managed by Titan, and there can be no assurance that the investments will be profitable or that other investments made in the future will have similar characteristics or results.

Charts and graphs provided within are for informational purposes solely and should not be relied upon when making any investment decision. Past performance is not indicative of future results. The content speaks only as of the date indicated. Any projections, estimates, forecasts, targets, prospects, and/or opinions expressed in these materials are subject to change without notice and may differ or be contrary to opinions expressed by others. Please see Titan’s Legal Page for additional important information.

Three Things, a newsletter from Titan

Stay informed on the most impactful business and financial news with analysis from our team.

You might also like

How to Calculate Rate of Return on Investments

Rate of return allows us to make clear comparisons among investments, which is essential. It puts them on a common scale.

What Is Compound Interest?

Compound interest works by using the continual multiplication—or compounding—of an amount of money, over a set number of cycles, within a set period of time.

What Is a Rate of Return?

Simply put, the rate of return (ROR) is the gain or loss for any investment, in percentage terms, for a given period of time.

What Is Annual Percentage Rate (APR)?

The APR takes into account interest rate and any fees a lender may charge for issuing a personal loan or mortgage, or for credit cards, any unpaid balance.

Cash Management

Smart Cash

Smart Cash FAQs

Cash Options

Get Smart Cash

Titan Global Capital Management USA LLC ("Titan") is an investment adviser registered with the Securities and Exchange Commission (“SEC”). By using this website, you accept and agree to Titan’s Terms of Use and Privacy Policy. Titan’s investment advisory services are available only to residents of the United States in jurisdictions where Titan is registered. Nothing on this website should be considered an offer, solicitation of an offer, or advice to buy or sell securities or investment products. Past performance is no guarantee of future results. Any historical returns, expected returns, or probability projections are hypothetical in nature and may not reflect actual future performance. Account holdings and other information provided are for illustrative purposes only and are not to be considered investment recommendations. The content on this website is for informational purposes only and does not constitute a comprehensive description of Titan’s investment advisory services.

Please refer to Titan's Program Brochure for important additional information. Certain investments are not suitable for all investors. Before investing, you should consider your investment objectives and any fees charged by Titan. The rate of return on investments can vary widely over time, especially for long term investments. Investment losses are possible, including the potential loss of all amounts invested, including principal. Brokerage services are provided to Titan Clients by Titan Global Technologies LLC and Apex Clearing Corporation, both registered broker-dealers and members of FINRA/SIPC. For more information, visit our disclosures page. You may check the background of these firms by visiting FINRA's BrokerCheck.

Various Registered Investment Company products (“Third Party Funds”) offered by third party fund families and investment companies are made available on the platform. Some of these Third Party Funds are offered through Titan Global Technologies LLC. Other Third Party Funds are offered to advisory clients by Titan. Before investing in such Third Party Funds you should consult the specific supplemental information available for each product. Please refer to Titan's Program Brochure for important additional information. Certain Third Party Funds that are available on Titan’s platform are interval funds. Investments in interval funds are highly speculative and subject to a lack of liquidity that is generally available in other types of investments. Actual investment return and principal value is likely to fluctuate and may depreciate in value when redeemed. Liquidity and distributions are not guaranteed, and are subject to availability at the discretion of the Third Party Fund.

The cash sweep program is made available in coordination with Apex Clearing Corporation through Titan Global Technologies LLC. Please visit www.titan.com/legal for applicable terms and conditions and important disclosures.

Cryptocurrency advisory services are provided by Titan.

Information provided by Titan Support is for informational and general educational purposes only and is not investment or financial advice.

Contact Titan at support@titan.com. 508 LaGuardia Place NY, NY 10012.