http://www.twincommas.com/how-to-double-your-money-the-rule-of-72 Wealth, Money, and Entrepreneurship Fri, 09 Jul 2010 20:07:35 +0000 hourly 1 http://wordpress.org/?v=3.0 http://www.twincommas.com/how-to-double-your-money-the-rule-of-72/comment-page-1#comment-207 David Fri, 09 Jul 2010 20:07:35 +0000 http://www.twincommas.com/how-to-double-your-money-the-rule-of-72#comment-207 Thanks for the explanation. The only quibble I have is that your reasoning of why 72 is used instead of 69.3 (or 69, or 70) is not too convincing. No doubt 72 is easier to use in mental arithmetic than 69.3, but it's less obvious that it's easier to use than 70. The real reason is that 72 is more accurate for the values of r that are likely to arise in actual calculations. For r=5%, ln(1+r) = .9758*r and for r=10%, ln(1+r)=.9531*r So for 5% interest 71.0 would be a much better number to use than 69.3, and for 10% interest 72.7 would be better than 69.3. So for a wide range of realistic interest rates, 72 leads to superior approximations than 69.3. Thanks for the explanation. The only quibble I have is that your reasoning of why 72 is used instead of 69.3 (or 69, or 70) is not too convincing. No doubt 72 is easier to use in mental arithmetic than 69.3, but it’s less obvious that it’s easier to use than 70. The real reason is that 72 is more accurate for the values of r that are likely to arise in actual calculations. For r=5%, ln(1+r) = .9758*r and for r=10%, ln(1+r)=.9531*r So for 5% interest 71.0 would be a much better number to use than 69.3, and for 10% interest 72.7 would be better than 69.3. So for a wide range of realistic interest rates, 72 leads to superior approximations than 69.3.

]]>