Dispelling long-term mirages with the Rule of 72


By Clark Troy

It was Einstein who said, “Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t pays it.” But it is Warren Buffett of Berkshire Hathaway, everyone’s favorite adopted financial uncle, who has been most prone to lapse into ecstatic revery on the virtues of compounding, particularly when paired with long periods of time, famously declaring that his wealth “has come from a combination of living in America, some lucky genes, and compound interest.” This formula works for anyone: if one can acquire and hold assets for a long time and let them appreciate at decent rates of return, they increase in value astonishingly and inexorably. Then again, often, the long periods of time part of this equation can actually be so magical that it creates an illusion of returns that appear better than they in fact are.

Here’s where one of the most fruitful concepts in applied math, the Rule of 72, comes into play. For those of you who – like me – never learned about the Rule of 72 in school, it means that if you multiply something’s rate of growth times the number of periods over which it has grown and the product is 72, it roughly doubles. So $10,000 growing annually at 6% doubles in about 12 years (6 X 12 = 72), whereas if it grows at 8% it doubles in 9 years (8 x 9 = 72). A population growing at 4% doubles in 18 years or so. Inflation of 3% cuts the purchasing power of a dollar roughly in half in 24 years.

There’s a similar number for how long it takes for something to grow by 50%, which we can call the Rule of 42. Something growing at 7% annually will increase by 50% after 6 years (7 x 6 = 42) and before doubling in a little more than 10.

If you can hold these two formulas in your head and apply them, you can estimate quickly and make sense of things. Let’s look at the story of a house because houses are often people’s favorite investments because they are tangible, and people see such large gains in them. The parents of some friends of mine bought a house in 1974 for a little more than $20,000 and sold it for about half a million in 2019. Sounds brilliant, right? Let’s do some back-of-the-envelope math using our rules. The house doubled in value four times (to $ 40k, $80k, $160k, and finally $320k) and then went up a little more than 50% from there (from $320k to $500k). So if we multiply 72 x 4 for the four doublings, we get 288. Add 42 for the last growth by 50%, and we will have 330. Divide 330 by the number of years they were in the house (45), and we get 7.33, which we know is a little low because to get from 320 to 500 is a little more than 50%. If we calculate the precise rate of return on the house using a financial calculator, the actual rate of growth to go from 20 to 500 over 45 periods is 7.42%. Our “a little more than 7.33%” estimate was spot on.

But was it a good investment?  Bearing in mind that 1974 was a very bad year in the stock market and 2019 a very good one, total returns on the S&P 500 from 1974 to 2019 are 11%-12% (depending on which month you start), slightly better than the index’s long term average of 10.5%. Let’s use the rule of 72 to estimate those returns. If we use the 11% number that tells us the investment would have doubled every 6.5 years (6.5 x 11 = 71.5), so dividing the 45 years by 6.5 gets us something just shy of 7 periods of doubling. So the original $20k would have doubled slightly fewer than 7 times. Multiplying our original $20k by a little less than 27 or 128 times gives us an estimated $2.25 million, quite close to the actual ~$2.19 million figure.

Of course, there are many caveats here comparing the returns on investments in a primary home vs. in the stock market. The primary home has the positive attribute of preferential capital gains as well as the fact that most are bought with mortgages so the actual gain one should count is arguably not going from $20k to $500k but from $4k (the downpayment) to $500k (assuming the mortgage has been paid off). One also has to remember the high transaction costs of buying and selling a home, historically hovering around 6%. However, the recent decision and settlement concerning broker commissions may reduce this over time. Homeowners also pay mortgages, taxes, insurance and maintenance costs, the analogs of which are bundled into rent for those who choose to invest their principle in capital markets, so ongoing expenses are more or less a wash when comparing real estate and capital market investing.

But we have digressed. Our main point with this example was not to do a fine-grained comparison between investing in a primary home and in the stock market, but the fact that the long holding periods often associated with owning a primary homes and people’s lack of familiarity with time value of money calculations creates an optical illusion of returns better than they actually are. If you understand the Rule of 72 (and that of 42) and how to estimate compound returns quickly, you can cut numbers down to size.

One more codicil: I would never argue against home ownership for one’s primary residence if you know you’re going to be in an area for a while. A host of intrinsic benefits derive from owning one’s own home. The real problems start when people are deluded by long holding periods and the fact that they’ve owned a house into thinking they understand real estate as an asset class. Most people don’t. I know I don’t. Real estate investing almost always involves leverage and risks that are hard to see. People muscle past them in their own beloved homes but all too often take baths when investing in second ones.

And again, keep the Rules of 72 and 42 in mind whenever you’re thinking about rates of growth. You’ll find them surprisingly handy.

Clark Troy was born in Durham and educated in the Chapel Hill-Carrboro City Schools, then elsewhere. He is a financial planner at Red Reef Advisors and may be reached at clark.troy(at)redreefadvisors.com. When not working, he reads, plays sports, naps, drinks coffee and plays guitar, not necessarily in that order.
This reporter can be reached at Info@TheLocalReporter.press

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