10x Compounding and an Exercise for the Student

Most investors are familiar with the “Rule of 72,” a formula for approximating the time it takes an investment to double at a given compounded annual return. The rule states that dividing 72 by the annual return equals the number of years to double. Conversely, the Rule of 72 can also determine the annual return by dividing 72 by the number of years. For example, it takes nine years to double an investment compounding at 8% a year (72/8% = 9 years). Similarly, the return required to double an investment in just six years is 12% (72/6 years = 12%).

Retirement is the primary goal of many investment plans. These long-range plans require more than just a doubling of an investment and involve time horizons that are longer than those easily estimated with the Rule of 72. Instead of Rule of 240 Compoundingincreasing your investment by 2x, what if you wanted to increase it 10x? To make the planning process easier, I developed the “Rule of 240, a formula for approximating the time and/or compounded return needed for an investment to increase by a factor of 10, or 10x compounding. The mathematical term for a factor of 10 is called an “order of magnitude.” It may be easier to think about it as “adding a zero” to your investment.

The methodology for using the “Rule of 240 Compounding is the same as the Rule of 72. Namely, the number of years it takes to increase an investment by an order of magnitude, multiplied by the annual return is equal to 240. For example, an investment will take 20 years to add a zero ($100 will grow to $1,000) if the return is 12% a year (240/12% = 20 years).  With an 8% annual return, it will take an investment 30 years to increase by a factor of 10.

Although the Rule of 240 is an estimation technique for 10x compounding, it is a reasonably accurate estimate. The Rule of 240 is accurate to within six months for all returns in the 6% to 15% range and is accurate to within 0.1% a year for all periods greater than 21 years.

What about inflation and taxes? The previous description referred to an “investment” gaining 10x, but in reality, the rule applies to anything in nature that compounds—including inflation.

Inflation at 3% a year would be 10x after 80 years (240/3). Or, if you prefer to think of it in terms of diminishing value, then your $1 will be worth only 10 cents in 80 years at 3% inflation. If a new car cost $4,000 in 1966 and $40,000 today, then automobile inflation can be estimated to be 240/50, or about 4.8% a year for the past 50 years. Granted, today’s $40,000 vehicle has more bells and whistles than a 1966 model, but the math behind the estimate is still valid.

As for inflation-adjusted investment returns, the Rule of 240 still applies. However, you will need to adjust the “nominal” return for the after-inflation “real” return. For example, a 12% nominal return takes 20 years to increase 10x. With 3% inflation, your 12% nominal return becomes a 9% real return, and the number of years to achieve a 10x inflation-adjusted return becomes 240/9= 26.7 years.

Tax impacts can be estimated in a similar fashion. If you are “paying taxes” as you go, then simply use your after-tax annual return instead of the nominal return. If you adjust your nominal return for both inflation and taxes, be prepared for disappointment because your time to achieve a 10x increase just became much longer.

You can also use the Rule of 240 to provide a reality check to anyone that believes a $100k investment account is going to magically turn into a $1 million retirement fund at 5% a year. With zero inflation, that lofty goal requires about 48 years (240/5). With 3% inflation, that 5% nominal return becomes only a 2% real return, and the time required to achieve 10x quickly extends to multiple lifetimes (240/2 = ??, the answer is left as an exercise for the student)

Note: This is an updated version of the article I first published in July 1999, and an expanded version of the Rule of 240 published in March 2015.

An Exercise for the Student

Each week I bring you my standard three-part EdgeCharts showing the momentum and relative strength rankings for sectors, factors, and global categories. I attempt to highlight any noteworthy changes and provide my analysis on the significance of those changes. Additionally, I monitor the overall structures for trend shifts, rotations, and specific market-environment patterns.

Today, we are doing something different. Instead of a single chart, I’m bringing you two of them: last week’s chart and today’s chart. Additionally, I am not going to provide any commentary or analysis on the changes. Today, it is up to you to decipher and analyze the variations. Or as they say, “the rest is left as an exercise for the student.” If you forgot what I said last week, you can read it here. In case you are worried—don’t be. I’ll be back next week with my regular insights.



The charts above depict both the relative strength and absolute strength of various market sectors, styles, and geographic locations on an intermediate-term basis. Each grouping is sorted (top to bottom) by relative strength. The magnitude of the displayed RSM value is a measure of absolute strength, which is our proprietary method of measuring and reporting the intermediate-term strength as an annualized value.

“Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.”

—Albert Einstein

© 2016 Dynamic Performance Publishing, Inc. – All Rights Reserved. This material is protected under U.S. copyright law and is provided for the exclusive use of our members for personal purposes. Although our employees may answer your general customer service questions, they are not licensed under securities laws to address your particular investment situation. No communication by Dynamic Performance Publishing or our employees to you should be deemed as personalized investment advice. Any investment recommended in this email should be made only after consulting with your investment advisor and only after reviewing the prospectus or financial statements of the company. Dynamic Performance Publishing, its affiliates, and clients may hold positions in the recommended securities. Results are not indicative of holdings for clients of Flexible Plan Investments. Forwarding, copying, or otherwise duplicating this information for the use by anyone other than the intended recipient is expressly forbidden. Any retransmission of this material by you is your authorization to us to debit your credit card, or otherwise bill you, for a full price one-year membership for each violation. It may also cause your membership to be revoked without a refund. Any such action on our part does not prevent us from seeking additional legal remedies.

Subscribe to the Invest With An Edge weekly newsletter

And receive our special retirement report, Living on a Million-Dollar Portfolio

Subscribe to receive the Invest With An Edge weekly newsletter and receive our special retirement report, Living on a Million-Dollar Portfolio

Please provide your information below:

* indicates required
Please add info@allstarinvestor.com to your Address Book or Contacts to ensure you are receiving your newsletter to your inbox.

Sign up for our investment advisory service, All Star Investor:

Explore AllStarInvestor.com and improve your ETF game

Check us out on twitter:

Follow us on twitter

  • Categories

  • Tags