# What is the Rule of 72?

TheÂ Rule of 72 is a fast way to estimate the time it will take anÂ investment to double in value.Â This back-of-the napkin formula is a good way to compare twoÂ investment opportunities, identify the best place to put your money for optimal growth,Â examine the potential outcomes of fees or inflation, and more.Â

## TheÂ Rule 72Â Formula

TheÂ Rule of 72Â formulaÂ is straightforward and easy to use.

SimplyÂ divideÂ 72Â by theÂ interest rate or anticipated rate of return on an investment,Â andÂ voila!Â The result is the number of years you can expect it to take for that investment, loan, or otherÂ number that grows at a steady, compounding rate to double.Â

Where:
InterestÂ Rate = the rate of return on an investmentÂ

Letâ€™sÂ take a look at a brief example.Â

### The Rule of 72 in Action

An investment in XYZ Corp. has historicallyÂ (over the last decade)Â yieldedÂ a healthy 7Â percentÂ return. If we want to make an investment in it now, how long will it take for our money to double?Â

Plugging our numbers into the equation,Â we can see that if that 7Â percentÂ rate staysÂ constant,Â we can expect to double our money in a little over a decade:Â 72/7 = 10.29.Â

Note that weÂ enter the interest rate (rate of return) as a whole number larger than the numberÂ 1. If we enteredÂ 7Â percent into the denominator as .07,Â the answer would beÂ in excess ofÂ a thousand yearsâ€”not the kind of timeÂ frame most investors have in mind.Â

Here are some benchmarks you can use to guestimate the amount of time it will take an investment to double,Â without having to do any calculations at all.Â

Click or tap to enlarge

Armed with this quick and dirty estimate,Â we can easily compare any investments with a stable rate of returnâ€”butÂ thatâ€™sÂ not all.Â

Using theÂ Rule of 72,Â we can also determine that aÂ personal loan with a fixed interest rate of 8Â percentÂ and a principalÂ of \$4,000 will have grown to \$8,000 inÂ nine years if allowed to grow uncheckedÂ (72/8 =Â 9).Â ItÂ can tell us that an inflation rate of 3Â percentÂ will halve the value of our moneyÂ inÂ 24Â years (72/3 = 24).Â

In fact, any numbers that will grow at a steady rate canÂ halveÂ the length of time it will take for them to double (or halve) in size.Â This applies to populations,Â macroeconomicÂ conditions such as GDP (gross domestic product), and other interesting cases outside the world of investing.

## WhatÂ Does the Rule of 72Â Mean for Investors?

BesidesÂ basic comparisons between investments, theÂ Rule of 72 has some other interesting insights to offer investors.Â Though the simplified version we are talking about here is straightforward to use, theÂ conceptÂ behind itÂ originates from a more complicated logarithmicÂ formula.Â

By opting to use the simplified version,Â we lose some precision and accuracy in calculation, but not so much that the calculation ceases to be useful. Additionally, it is outside the scope of many investorsâ€™ experience to useÂ log tables or scientific calculators to determine the exact month, day, hour, and minute that their investment will double inÂ size.Â

Nevertheless, the concept behind theÂ Rule of 72 is an important factorÂ inÂ shapingÂ the way we think about different money opportunities.Â

### The Rule of 72 and Savings AccountsÂ

It is often said that if you scrimp and save and sock away every extra penny into your savings account,Â you will be surprised to find thatÂ itÂ hasnâ€™tÂ grown much at all,Â come year end. While savings accounts can be an important part of a personal money management plan, they are generally poor money-growthÂ vehicles.Â

Many savings accounts offer interest rates lower thanÂ 1Â percent. WeÂ intuitivelyÂ knowÂ this is a small amount, but when put into perspective via theÂ Rule of 72, we can see that it will take 72 yearsâ€”roughly the average lifeÂ span of most elephantsâ€”to double in value,Â assuming no other deposits were made.Â

## Is the Rule of 72 Accurate?

Rule of 72 calculations are sufficiently accurate for mostÂ investments with aÂ low rate of return.Â AsÂ withÂ all quick and dirty calculations,Â it isnâ€™tÂ perfectÂ and it shouldnâ€™t be relied upon as the soleÂ determining factor in deciding where to invest your money.Â

This is especially true forÂ investments withÂ high rates of return.Â

The accuracyÂ of theÂ Rule of 72 calculationÂ starts to break downÂ as the rates of return get largerÂ than the 10 percent mark.Â A general rule of thumb is thatÂ investors shouldÂ add 1 to 72 for every three percentage pointsÂ past an 8Â percentÂ rate of return. This would mean that to determine the most preciseÂ amount of time it would take an investment with an 11Â percentÂ rate ofÂ return,Â the formula would divide 73 by 11 instead ofÂ using 72 in the numerator.Â

Bearing this pattern out,Â the amount of time an investmentÂ with a 14Â percentÂ rate of return would take to double would be determined by dividing 74 by 14. For most investors, however, the fast and simpleÂ Rule of 72 is a sufficiently accurate calculation.Â

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