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Premature Optimization is a Prerequisite for Success

The Rule of 72 revised

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Wanna double your wealth? Invest it at r% rate and wait for 72/r years.

This is the well-known Rule of 72. Why does it work and what is 72 anyway?

72 because for r =0.08, r*log(2)/log(1+r) = 0.720… And 72 = 2^3*3^2 is a well-divisible number 🙂

And it works for other values of r because x/log(1+x) is almost perfectly linear between 0 and 1: http://www.wolframalpha.com/input/?i=x%2Fln%281%2Bx%29+from+0+to+1

But is r = 0.08 (8% rate) a safe assumption these days? 😉

Short-term treasuries rate is 0.007 today… let’s see 0.007*log(2)/log(1.007) is approximately 0.7 (I love the 3 sevens in this formula), so the revised risk-free rule is the rule of 70:

Wanna double your wealth risk free? Invest it at r% rate and wait for 70/r years.

At the high-risk rate you’ll have to wait for 72/8 = 9 years, and at the low-risk rate: 70/0.7 = 100 years.

And the general rule is: if you want to increase your wealth by the factor f, invest at the rate r and wait for log(f)/log(1+r) years.

Disclaimer: this should not be relied on as investment advice, and I shall not be liable for any direct, indirect, exemplary, compensatory, punitive, special or consequential damages, costs, expenses or losses 🙂 🙂 🙂

 

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Written by bbzippo

01/06/2011 at 3:45 am

Posted in fun, math

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