I remember learning, way back in junior high school, about how compound interest works. But for some reason I'm never able to remember the silly little formula for figuring out how long it takes to double an investment, given a fixed rate of annual return.

So here's a quick reminder.

The "Rule of 72" says that you take the interest rate (assuming that it's compounded annualy) and divide 72 by it. For an investment that yields 7% annual returns, that means 72 / 7 which is roughly 10.3 years.

Here are a few more:

- 5%: 14.4 years
- 6%: 12 years
- 7%: 10.3 years
- 8%: 9 years
- 9%: 8 years
- 10%: 7.2 years
- 11%: 6.5 years
- 12%: 6 years
- 15%: 4.8 years
- 20%: 3.6 years
- 25%: 2.9 years

Anyway, I'm hoping that the act of taking two minutes to write this down will make it stick in my brain a bit longer.

Now... anyone wanna loan me half a million dollars and an investment with a 20% annual return? :-)

Posted by jzawodn at June 12, 2005 08:44 AM

**Rory Parle**said:

In case you're interested--and since it's not that interesting I can only assume you're not--the correct formula is N = ln(2) / ln(1 + (I/100)), where N is the number of years it takes to double and I is the interest rate. Since ln(1 + x) ~= x for low x it gets reduced to N = ln(2) * 100 / I, or N = 69 / I. That's only an approximation and I assume the higher number of 72 is used because it approximates better at the rates usually used for interest which is slightly too high for my approximation.

**James Kew**said:

A bit of dinking around in a spreadsheet confirms Rory's suggestion: Rule of 72 is a better approximation for typical interest rates than the true I-->0 Rule of 69.

Rule of 69 is more accurate for rates 3% and below; Rule of 72 gives results accurate to within 2% for rates between 4% and 12%.

They both fall off in accuracy at high rates. But if you're getting a 25% return, you're probably not that bothered about the difference between 2.9 years and 3.1 years...

**Mike**said:

> anyone wanna loan me half a million dollars and an investment with a 20% annual return?

CC me too!

**Michael Parekh**said:

cool post...always good to get a reminder on things you know you learned many times in your life, forgot again, but need a kick in the memory to remember again...

google should also add this to their web calculator offerings.

Strangely, I initially found your blog when I googled for the title/term, "Your Money or Your Life". As I recall, you didn't like the book (nor did I), but there is some validity to the underlying message.

Start investing at an early age, don't do anything too stupid (in terms of investing), and you'll retire comfortably.

Based on how low current interest rates (and the stock market's return) have been in recent years, it's more important than ever.

**Mike Woodhouse**said:

I think another reason for using 72 instead of some possibly more accurate number is that it's a fairly good number to divide things into.

If you have something capable of electronic calculation handy, the rate you need for doubling over any period of N Years is just the Nth root of 2 (or whatever multiple you're seeking) less one.

So to triple your money in seven years, you calculate 3^(1/7) (to use Excel as an example) and get 1.16993, which translates to 16.993% annually.

**GrumpY!**said:

the fact that no one here said the word "tax" tells me how many of the posters have experience managing large investments.

**George**said:

As an Investment Advisor Representative, I think...

We ought to give the credit to Albert Einstein (yep, THAT guy) who developed the 'Rule of 72' - he said it was his most important discovery - ever.

And that if you DON'T know how to make 20% a year, you should find an Investment Adviser Representative.

**Larry**said:

So I guess if you find an investment that pays 72% interest, you'll double your investment in one year (smile).

**AK**said:

But 72 % are much more than the 12 % (see discussion of James Kew) ...

**Jerry**said:

72 works great. It works even better if you compound daily instead of monthly. What about Uncle Sam? I believe the number then changes from 72 to 102. So, if you want to figure out how long it will take to double your money if you have to pay an annual tax on the money of 30%, divide 102 by the interest rate and you should be pretty close. Thanks Uncle Sam... You're the best! If the opposite of pro is con then the opposite of progress is congress.

**Jet**said:

Hah! I know of a stock that's currently paying 21% dividends vs. its price (took a beating being a financial sector item, but otherwise is a healthy company poised for good growth.) ... so even if the price remained static for 3.5 years or so, you'd still double your money! Assuming the dividend remains static as well.. (and for the last few years it has only gone up, even in spite of recent market downturns.) Not sure if I can say what it is, but with any old stock browser, that kind of dividend level will stick out like a sore thumb =)

Good luck mang, thanks for the 72 thing!

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