11 ms·
The Rule of 72 (2007)
- tristanj 10y agoMy Economics 101 professor in university taught this in class, and told us that if we only remembered one thing from his class, it should be this.
- shoover 10y agoIt's the one thing I remembered from my high school US Government teacher. (Or was it Sociology? Same teacher, two classes. What's up, Mr. Swigert?) I always thought it was really cool that he taught us that and it stuck. It had nothing to do with the lesson of the day, he just did it.
- cperciva 10y agoIn addition to being nicely divisible, 72 has an important advantage which most people don't realize: It's on the right side of 100 ln(2). The exact "rule" for N% interest is N log(2) / log (1 + N/100), which has taylor series 100 log(2) + log(2)/2 N + O(N^2) ≈ 69.315 + 0.34657 N - 0.0005776 N^2 + ... For N approaching 0, the exact "rule" becomes the "rule of 100 log 2"; but for larger N increases slightly; the "rule of 72" is exactly correct for ~7.84687% interest, and for 15% interest it only gets as far as a "rule of 74.4". That said, the power series gives us a way to get a significantly more accurate result: Divide the annual percentage interest rate into 832 months, then add 4 months. For any interest rate between 1% and 40%, this result will be accurate to within 3 days.
- jessriedel 10y agoThat doubles the attractiveness of this rule of thumb. Too bad the author left it out.
- kalid 10y agoNeat insight, I'll add it in :).
- kalid 10y agoThanks Colin, just added :). (Aside: I love how useful text is a medium. In 5 minutes I can put in a quick insight to improve a decade-old article.)
- patrec 10y agoMaybe I'm obtuse but I'm not sure I understand what you mean by the "right side". You definitely want to use a number that's slightly larger than 100 ln(2) ~= 69.3 to account for the linear factor, but is there some inherent reason to use 72 rather than say 70 or 74, other than that assuming that 8% is some useful midpoint for the type of growth rates you're likely to be interested in?
- AnimalMuppet 10y agoI believe the point was, don't use 68 or 64.
- kalid 10y agoI think that's what he meant; round up (not down) because the next correction term in the series is positive. 72 is better (mentally) than 70 or 74 because it has more divisors.
- cperciva 10y ago72 is better than 70 or 74 because it's divisible by more small factors. My point was that it's fortunate that 72 is slightly more than 100 log 2 rather than slightly less; for "how long will it take for money to triple" (100 log 3 = 109.86) taking the closest number with lots of divisors would lead you to take a "rule of 108" but since 108 is slightly less than 100 log 3 instead of slightly more, it will produce larger errors for the common range of interest rates.
- JumpCrisscross 10y agoI never understood how ten percent errors, when applied to decades by creatures who expire in decades, were acceptable. This is a great approximation trick, but as with most things, please understand its derivation. Most of the time when I see the "Rule of 72", it's in Excel spreadsheets. I passed on investing in an infrastructure project by changing a Rule of 72 calculation to: YearsToDoubling = ln(2) / ln (1 + Rate) and watching it cascade to a negative NPV.
- Ntrails 10y agoIt's a great trick for approximating a value with mental maths. When my boss says he thinks the team can double revenues over 5 years - I can pretty quickly see what sort of year on year growth he's magically assigned. When you're in a goddamned fancy calculator, you do the full form calculation because what the hell. I mean, I don't understand why you'd be deriving NPV from "years to doubling", but you can sure as hell get it exact. (Also, as someone who's never actually invested, do people really judge investments on that number rather than internal rate of return, payback period, etc etc?)
- JumpCrisscross 10y ago> do people really judge investments on that number rather than internal rate of return Internal rate of return (IRR) is the rate at which the net present value (NPV) of a set of cash flows is zero. NPV is, in essence, a scaled IRR. If you have a budget of capital to deploy, NPV is preferred. For example, if you have a $100MM budget with a cost of capital equal to zero and two investment options: a $10MM project yielding 20% and a $100MM project yielding 10%, and you cannot purchase parts, only wholes (see the appeal of securitisation?), then IRR would guide you to the former while NPV to the latter. When dealing with securities or any other sufficiently quantised investment, IRR becomes a good enough approximation.
- Ntrails 10y agoI was more referring to "Time to doubling" as a metric for investment analysis, IRR/NPV I am comfortable with academically.
- pkd 10y agoI first heard of this rule in the seminal book, Programming Pearls. In case you have not yet read it, please do.
- edward 10y agoI just read about the Rule of 72 in a book titled The Intelligent Asset Allocator: How to Build Your Portfolio to Maximize Returns and Minimize Risk by William Bernstein. It is a good book, I recommend it.
- coolvoltage 10y agoThe same blog has an interesting explanation of the 80/20 rule http://betterexplained.com/articles/understanding-the-pareto-principle-the-8020-rule/ http://betterexplained.com/articles/understanding-the-pareto...
- deleted 10y ago[deleted]
- golergka 10y agoThis is a neat trick, but why would we need to approximate something that is so easy to calculate in the first place?
- adrianratnapala 10y agoIs it easy to calculate in your head?
- croon 10y agoI think he's asking under the (reasonable) assumption that everyone has a smartphone handy.
- sokoloff 10y agoFor a great many business discussions, a close enough answer that's technologically unaided is way more effective than a precise answer that takes an extra 45 seconds and the incorporation of a smartphone (or one person per smartphone) into the discussion. I think of it as akin to the fluidity of a conversation between two native speakers versus a conversation with a translator in the room.
- delazeur 10y agoYou save a bit of time and you look pretty smart. I can do calculus in my head, but I struggle with arithmetic. My colleagues who can do fast mental math but can't do any algebra to save their lives end up looking much more competent in meetings.
- ricardobeat 10y agoAssuming 6% annual interest, what would be the "easy" equivalent of 72/6?
- MandieD 10y agoIt's good to have a feel for the rate of increase when reading news articles or having a vague idea what an interest rate really means, just like knowing scientific notation helps you get a quick feel for the difference between a government program costing 550 million and one costing 5.3 billion, compared to a country's GDP of 1.2 trillion. By the way, betterexplained.com is where I finally, after memorizing my way through just enough calculus to get a BS in comp sci, began to understand calculus. Seeing how the area of a circle was derived was wild - I'd easily memorized all that stuff, but never understood. We wait way too long to begin teaching calculus concepts.
- nailer 10y agoPeople shouldn't be able to get credit cards until they understand compound interest. This stuff should be taught in high schools. There's a group doing that: http://schooold.com/ http://schooold.com/. They have a financial curriculum that's now part of the Kitty Andersen Youth Science Center.
- collyw 10y agoIf people can't understand compound interest there are probably many things they shouldn't be doing. Its not a difficult concept.
- dforrestwilson 10y agoYour point reinforces the OP case. It's not particularly difficult, and yet it's very important to life after school. High schools should have a mandatory personal finance class.
- Avshalom 10y agoCompound interest gets taught in like middle school. The same time we get taught percents and stuff. That said "compound interest" is and any sort of interest is kind of futile if, like a credit card, the principle is constantly changing, it's also a bit hard to scare people into frugality by telling them if they put these steaks on credit they'll have to pay $12 dollars more later. The numbers don't get scary until well into "they already knew they shouldn't do it" territory.
- salimmadjd 10y agoI think the concept is easy to grasp, but seeing the impact of 30% with actual numbers is very different. It makes the financial impact more comprehensible.
- taneq 10y agoSpending all of your time with people in the top few percent, intellectually, tends to skew your perceptions of what's normal. Most humans struggle with concepts like compound interest. There's a reason hating highschool maths is a trope, despite how trivial most of it is.
- guard-of-terra 10y agoThe rule of 7% is more potent and easier to understand. It tells you that if market grows by 7% annually, it's going to move more volume in ten years than in all years before, combined. For example, of country's electricity consumption grows by 7% YoY, it's going to consume more electricity in (any) ten years than it ever consumed before that, grand total.
- JTon 10y agoI fail to see how you can compare the two rules of thumb. For starters, the rule of 72 is simply talking about doubling (not about aggregate consumption)and the rule of 72 isn't fixed to a single interest rate (7%).
- amelius 10y agoI'm still wondering why there are 72 points in an inch. Probably only because it is nicely divisible.
- jjallen 10y agoGlad to see this rule come up on a tech site. This is Finance 102 stuff and it's good for everyone to know. Just in case this hasn't been said elsewhere, the rule is more precise for numbers whose factor into 72 is closer to it. So medium numbers, for lack of a way of saying it. Not 50, not 1, but 12, 8, etc.
- pieguy 10y agoI prefer the approximation (4+832/N), which gives its result in months. Not as easy to do in your head but it's quite accurate.
- acqq 10y agoRelated: "The Most IMPORTANT Video You'll Ever See" (it's an old youtube obviously click-bait-style title, but it's a video of a lecture worth watching, see the description): http://www.informationclearinghouse.info/article25458.htm http://www.informationclearinghouse.info/article25458.htm