# The Rule of K Vs Rule Of 72

This is a small update of my last piece.  I wish that I had put this graph in that piece, because it completes it.

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Over the interest rate range of 0% to 30%, the average absolute deviations from perfect doubling using the Rule of 72 was 2.794%.  Given the simplicity of the Rule of 72, that is wonderful.

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But the "Rule of K" is virtually exact.  The average absolute deviations from perfect doubling using the Rule of K was 0.036%.

Is this great?  Well, with modern computers, exactitude is easy to come by.  But if you are in a pinch to figure out the time to double, and all you have is a pencil and paper, the rule of K can do it with addition, subtraction and division.  No fancy powers or logarithms.  A four-function calculator will handle it, which, if you are using a rate that does divide into 72 easily, you will still need for the calculation.

At 8% the two are equal.  Near 8%, the Rule of 72 is pretty good.  The Rule of K gives an almost exact answer at the cost of a little complexity.  Your choice depends on whether you need exactness or simplicity when all you have to work with is a four function calculator.

The Rule of K: If R is the interest rate multiplied by 100, money doubles in K/R years, where K = 70 + (R – 2)/3

Article by David J. Merkel, CFA, FSA - The Aleph Blog

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David J. Merkel, CFA, FSA — 2010-present, I am working on setting up my own equity asset management shop, tentatively called Aleph Investments. It is possible that I might do a joint venture with someone else if we can do more together than separately. From 2008-2010, I was the Chief Economist and Director of Research of Finacorp Securities. I did a many things for Finacorp, mainly research and analysis on a wide variety of fixed income and equity securities, and trading strategies. Until 2007, I was a senior investment analyst at Hovde Capital, responsible for analysis and valuation of investment opportunities for the FIP funds, particularly of companies in the insurance industry. I also managed the internal profit sharing and charitable endowment monies of the firm. From 2003-2007, I was a leading commentator at the investment website RealMoney.com. Back in 2003, after several years of correspondence, James Cramer invited me to write for the site, and I wrote for RealMoney on equity and bond portfolio management, macroeconomics, derivatives, quantitative strategies, insurance issues, corporate governance, etc. My specialty is looking at the interlinkages in the markets in order to understand individual markets better. I no longer contribute to RealMoney; I scaled it back because my work duties have gotten larger, and I began this blog to develop a distinct voice with a wider distribution. After three-plus year of operation, I believe I have achieved that. Prior to joining Hovde in 2003, I managed corporate bonds for Dwight Asset Management. In 1998, I joined the Mount Washington Investment Group as the Mortgage Bond and Asset Liability manager after working with Provident Mutual, AIG and Pacific Standard Life. My background as a life actuary has given me a different perspective on investing. How do you earn money without taking undue risk? How do you convey ideas about investing while showing a proper level of uncertainty on the likelihood of success? How do the various markets fit together, telling us us a broader story than any single piece? These are the themes that I will deal with in this blog. I hold bachelor’s and master’s degrees from Johns Hopkins University. In my spare time, I take care of our eight children with my wonderful wife Ruth.
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