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Tuesday, November 2, 2010

The Rule of 72

Last night's class was about inflation; and we talked a bit about what the CPI measures, how it is measured, and some of its shortcomings. During the class, I brought up the "rule of 72" mainly to show how long it takes for prices to double under given rates of inflation.

The rule of 72 is a good way to look smart, and one of the objectives in the work world is to convince people (especially your bosses) you're smart.

For example, if you tell me an investment will earn 4%/year, then I can tell you right away, off the top of my head, that it will double in 18 years. Pretty smart, huh?

To provide a practical application of the rule, I decided to spend a couple of minutes showing the results of saving at a young age.

The Rule
The rule is simple: 72 divided by a growth rate gives an answer on how long it will take for a magnitude to double. For example, if something is growing 8%/year, compounded, then the rule says 72 divided by 8 = 9 years. 9 years is the time it will take to double.

For homework, figure out how long it will take for a magnitude to double if it grows 4%/year.

The Lesson
Next, by a show of hands, I asked how many students were 20 years old; and most of the hands went up. That's what we worked with. I assumed an initial investment of $1,000 and an 8% average annualized compound return. By the rule of 72, that $1,000 will be $2,000 by the time the 20-year-old turns 29 years old.

We get the following:

29th birthday $2,000
38th birthday $4,000
47th birthday $8,000
56th birthday $16,000
65th birthday $32,000

If you think about this a little bit, you'll be able to understand why the dollar today is worth approximately one-fifth of what it was worth when I was in school (3 Musketeers bar cost $.25 versus $1.25 today). You'll understand Henny Youngman saying "the country's getting stronger - it used to take 2 adults to carry $20 worth of groceries, now a 5-year-old can do it." These, of course, are different ways of expressing inflation.

I let the class in on another piece of news. Subject to the workings of the Darwin awards, most of them would wake up one morning surrounded by friends and family with a birthday cake to celebrate their 65th birthday. This is not easy to grasp for a 20-year-old. It wasn't easy for me when I was 20.

The point is a basic one of personal finance: save when you're young and you don't have to save as much.

The corollary is: saving when you are young gives you choices when you are older. This is where a Walmart greeter as a guest speaker would be useful.

Additional Resource Interesting YouTube for those interested in critical thinking and learning more about the rule of 72.


  1. Nice article Robert. A powerful rule indeed. So, any lightbulbs go off last night? Or just some shoulder shrugging?

    I guess the challenge for all young folk, easy principle, difficult to consistently put into practice. Application is always more difficult than theory.

    I know I didn't start investing regularly for retirement until I was about 24, over 10 years ago.

  2. Some lightbulbs did go off. The disconcerting part was that this was the first time many had seen the impact of investing early. They just aren't exposed to personal finance in the high schools. It's too bad because this is a lesson that can fit into a math class lesson about logarithms for example.