The Rule of 72

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The explanation is so good!

You are a very good math explaner

@Clarafy: Thanks!

So, if one earns 3% a year but the inflation rate is 2%, then the actual is 72/1 = 72 years? Okay, assuming that is correct, what if the difference is 0? Inflation and earned interest are the same? Then 72/0 = ? So, after 20 years, you have the same investment value, but we know the value of money will decrease over time. How is that factored? thanks

Thats really cool.
You can also do the same thing with smallish percentage chance getting to 50%
E.g. each trial gives you 7% of “winning” how long to 50/50 chance?
Answer is also about 72/7
This works as ln(1/2) = -ln2
and here we start with (1-R)^N = 1/2
So the to negative will divide returning to you rule of 72

@Ben: Thanks, that’s a really neat application!

Can you source your comment about Einstein calling it the most powerful force…?

@MJ: Hrm, I can’t! I looked around and it seems it’s undetermined (according to Snopes, anyway) if Einstein really said it:

[…] The math behind the rule of 72 is easy to extend to triplings (rule of 110), quadrupling (rule of 140), quintupling (rule of 160), etc. […]

[…] The Rule of 72 Explained […]

i need answer for one question if possible please send the solution-
Q. A finance company offers to give Rs.8000 after 12 years in return for Rs.1000 deposited today. Using the rule 72 find out the approximate interest rate offered.

Do you have a simple method of understanding the rule of 78 (front loaded interest used for most auto loans to penalize early payment)

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[…] If you want a deeper dive, check out the technicalities of The Rule of 72. […]

“You can approximate ln(1+R) by just R”, sorry for the typo!

I read your site just to see what SOME of the different sites had to say about R of 72. I learned that about 25 years ago when working with A. L. Williams which is now Primerica. I have returned to Primerica after a long hietus, and math being my hight(est) point in school, love to be there, as I love to help people. Enough said. Thanks for the info that you have posted. May many many more read it!

thanks for this help!!!

@Enginerd (28 Apr 2008), 72 does work better than 69, it’s not just less dirty :slight_smile:

You can approximate log R by just R, but a better approximation is R - R^2/2, or R(1 - R/2). So, the magic number that we’re looking for will be 100*(log 2)/(1 - R/2). If we use R=0, then the formula will work best for an interest rate of zero, not very handy. If the usual range of interest rates is between 0 and 15%, then using a value in the middle would make the most sense. So, using 7.5% would mean that the magic number would be close for that whole range, and the formula would be nearly perfect near 7.5%.

100*(log 2) / (1 - 7.5%/2) = 72.01529…

That’s why we use 72 instead of 69.