THE RULE OF 72
=>A Method Of Estimating How Long It Will Take (In Years) To Double Your Money Using Compound Interest At A Given Rate.
=> A Method Of Estimating At What Rate Of Compound Interest It Will Take (In A Whole Number Percentage) To Double Your Money In A Given Number Of Years.
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.
These rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference, 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible. There are a number of variations to the rules that improve accuracy. For periodic compounding, the exact doubling time for an interest rate of r per period is
where T is the number of periods required. The formula above can be used for more than calculating the doubling time. If you want to know the tripling time, for example, simply replace the constant 2 in the numerator with 3. As another example, if you want to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.
You can amaze your friends and colleagues by doing compound interest computations in your head (or on a napkin, if you require one).
For example, the amount of time that is required to double your investment at a compound interest rate of 4% would be 72/4, or 18 years, while the time required to double your investment at a rate of 8% would be 72/8, or 9 years.
As another example, the rate of compound interest required to double your money in 5 years would be 72/5, or 14.4%, while the rate of compound interest required to double your money in 10 years would be 72/10, or 7.2% per year.
It’s a very good system for quick and dirty estimates of time and compound interest. Use it, and enjoy it.
Douglas E. Castle
Labels, Tags, Keywords, Categories And Search Terms For This Article: Rule of 72, computations, investments, ROI, compound interest, doubling money, The Braintenance Blog, Douglas E. Castle, math shortcuts, financial calculations, Douglas E. Castle Blog, Rule of 69, Rule of 70, Rules of thumb, capital recovery, the Payback Method.
NOTE: THE INFORMATION CONTAINED IN THIS ARTICLE SHOULD NOT BE CONSTRUED BY THE READER AS BEING LEGAL, FINANCIAL, TAX, ACCOUNTING, ECONOMIC OR INVESTMENT ADVICE. NO OFFERING OF SECURITIES OR OTHER INVESTMENT INTERESTS OF ANY TYPE IN ANY ENTITY IS MADE HEREBY, NOR IS A SOLICITATION FOR THE PURCHASE OF SECURITIES OR OTHER INVESTMENT INTERESTS OF ANY TYPE IN ANY ENTITY MADE HEREBY. THIS ARTICLE IS INTENDED FOR GENERAL INFORMATIONAL PURPOSES ONLY AND REPRESENTS THE VIEW OF THE AUTHOR ONLY.
THIS ARTICLE IS COPYRIGHT 2014 BY DOUGLAS E. CASTLE, WITH ALL RIGHTS RESERVED. ANY REPRODUCTION, TRANSMITTAL OR DISTRIBUTION OF THIS ARTICLE, EITHER IN WHOLE OR PART, IS UNAUTHORIZED AND MAY BE UNLAWFUL, UNLESS FULL ATTRIBUTION IS GIVEN TO THE AUTHOR AND ALL IMAGES AND LINKS IN THE ARTICLE REMAIN INCLUDED AND “LIVE.”
This site is proudly affiliated with Global Edge International Consulting Associates, Inc. ["GEI”]
Free Subscription to The GEI Business Daily!
Sign Up For Our Free GEI Newsletter!
Receive Our Free GEI RSS Feed!
***Follow GEI's Company Page On LinkedIn!