Rule of 72

Exponential growth - Examples 1 Compound interest at a constant interest rate provides exponential growth of the capital. See also rule of 72.

Bowling ball - Composition 1 The ABC established a shore durometer|durometer hardness rule of 72, which barred even some of the out-of-the- factory softer balls

Interest - Other conventions and uses 1 'Rule of 72': The Rule of 72 is a quick and dirty method for finding out how fast money doubles for a given interest rate. For example, if you have an interest rate of 6%, it will take 72/6 or 12 years for your money to double, compounding at 6%. This is an approximation that starts to break down above 10%.

Rule of thumb - Examples of usage 1 *'Statistical - Rule of 72': A rule of thumb for exponential growth at a constant rate

Luca Pacioli - Mathematics 1 He introduced the Rule of 72, using an approximation of 100*ln 2 more than 100 years before John Napier|Napier and Briggs.[ andrews.ac.uk/Extras/Pacioli_logarithm.ht ml St-and.ac.uk] A Napierian logarithm before Napier, John J O'Connor and Edmund F Robertson

Fra Luca Pacioli - Mathematics 1 He introduced the Rule of 72, using an approximation of 100*ln 2 more than 100 years before John Napier|Napier and Briggs.[ andrews.ac.uk/Extras/Pacioli_logarithm.ht ml St-and.ac.uk] A Napierian logarithm before Napier, John J O'Connor and Edmund F Robertson

Rule of 72 1 In finance, the 'rule of 72', the 'rule of 70' and the 'rule of 69' are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period to obtain the approximate number of periods (usually years) required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available.

Rule of 72 - Using the rule to estimate compounding periods 1 *For instance, if you were to invest $100 with compounding interest at a rate of 9% per annum, the rule of 72 gives 72/9 = 8 years required for the investment to be worth $200; an exact calculation gives ln(2)/ln(1+.09) = years.

Rule of 72 - Adjustments for higher accuracy 1 For higher rates, a bigger numerator would be better (e.g., for 20%, using 76 to get 3.8 years would be only about off, where using 72 to get 3.6 would be about 0.2 off). This is because, as above, the rule of 72 is only an approximation that is accurate for interest rates from 6% to 10%. Outside that range the error will vary from 2.4% to −14.0%. For every three percentage points away from 8% the value 72 could be adjusted by 1.

Rule of 72 - E-M rule 1 For example, if the interest rate is 18% the Rule of 69.3 says t = 3.85 years. The E-M Rule multiplies this by 200/(200-18), giving a doubling time of 4.23 years, where the actual doubling time at this rate is 4.19 years. (The E-M Rule thus gives a closer approximation than the Rule of 72.)

Rule of 72 - Other rules 1 Extending the rule of 72 out further, other approximations can be determined for tripling and quadrupling. To estimate the time it would take to triple your money, one can use 114 instead of 72 and, for quadrupling, use

Rule of 72 - Periodic compounding 1 Replacing the R in R/200 on the third line with 7.79 gives 72 on the numerator. This shows that the rule of 72 is most precise for periodically composed interests around 8%.

Doubling time 1 This time can be calculated by dividing the natural logarithm of 2 by the exponent of growth, or approximated by dividing 70 by the percentage growth rate (more roughly but roundly, dividing 72; see the rule of 72 for details and Rule of 72#Derivation|a derivation of this formula).

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