# The Rule of 72: Definition, Usefulness, and How to Use It

> **Definition**
>
> The Rule of 72 is a formula used to calculate how long your investment will need to double in value, given its annual rate of return.

## What Is the Rule of 72?

The Rule of 72 is a formula that's popularly used to estimate the number of years required to double invested money at a given annual [rate of return](https://www.investopedia.com/terms/r/rateofreturn.asp). Alternatively, it can compute the annual rate of [compounded return](https://www.investopedia.com/terms/c/compoundreturn.asp) from an investment, given how many years it will take to double the investment.

While calculators and spreadsheet programs have functions to accurately calculate the precise time required to [double the invested money](https://www.investopedia.com/financial-edge/0711/how-to-double-your-money-every-6-years.aspx), the Rule of 72 comes in handy for mental calculations to quickly gauge an approximate value. For this reason, the Rule of 72 is often taught to [beginning investors](https://www.investopedia.com/best-online-brokers-4587872), as it's easy to comprehend and calculate. The United States Securities and Exchange Commission (SEC) also cites the Rule of 72 in grade-level financial literacy resources.

### Key Takeaways

*   The Rule of 72 is a simplified formula that calculates how long it’ll take for an investment to double in value, based on its rate of return.
*   The Rule of 72 applies to compounded interest rates and is reasonably accurate for interest rates that fall in the range of 6% and 10%.
*   The Rule of 72 can be applied to anything that increases exponentially, such as GDP or inflation; it can also indicate the long-term effect of annual fees on an investment’s growth.
*   This estimation tool can also be used to estimate the rate of return needed for an investment to double given an investment period.

![Rule of 72](https://www.investopedia.com/thmb/YyGm-y2Dus_Rq1ylOAlaD8-8TjA=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Ruleof72-891af13fb6fe4acf89df0720aa50b340.jpg)

*The Rule of 72 can also be used for anything that grows at a compounded rate. — Investopedia / Daniel Fishel*

## Formula for the Rule of 72

The Rule of 72 can be leveraged in two different ways to determine an expected doubling period or required rate of return.

_Years to double = 72 / Expected rate of return_

To calculate the time period that an investment will double, divide the integer 72 by the expected rate of return. The formula relies on a single average rate over the life of the investment. The findings hold true for fractional results, as all decimals represent an additional portion of a year.

_Expected rate of return = 72 / Years to double_

To calculate the expected rate of interest, divide the integer 72 by the number of years required to double your investment. The number of years doesn't need to be a whole number; the formula can handle fractions or portions of a year. In addition, the resulting expected rate of return assumes compounding interest at that rate over the entire [holding period](https://www.investopedia.com/terms/h/holdingperiod.asp) of an investment.

> **Fast Fact**
>
> The Rule of 72 applies to cases of compound interest, not simple interest. Simple interest is determined by multiplying the daily interest rate by the principal amount and by the number of days that elapse between payments. Compound interest is calculated on both the initial principal and the accumulated interest of previous periods of a deposit.

## How to Use the Rule of 72

The Rule of 72 could apply to anything that grows at a compounded rate, such as population, macroeconomic numbers, charges, or loans. For example, if the [gross domestic product (GDP)](https://www.investopedia.com/terms/g/gdp.asp) grows at 4% annually, the economy will be expected to double in 18 years (72 / 4).

With regards to the fee that eats into investment gains, the Rule of 72 can be used to demonstrate the long-term effects of these costs. A mutual fund that charges 3% in [annual expense fees](https://www.investopedia.com/terms/e/expenseratio.asp) will reduce the investment principal to half in around 24 years. A borrower who pays 12% interest on their credit card (or any other form of loan that is charging [compound interest](https://www.investopedia.com/terms/c/compoundinterest.asp)) will double the amount they owe in six years.

The rule can also be used to find the amount of time it takes for money’s value to halve due to [inflation](https://www.investopedia.com/terms/i/inflation.asp). If inflation is 6%, then a given purchasing power of the money will be worth half in around 12 years (72 / 6). If inflation decreases from 6% to 4%, an investment will be expected to lose half its value in 18 years, instead of 12 years.

Additionally, the Rule of 72 can be applied across all kinds of durations provided the rate of return is compounded annually. If the [interest](https://www.investopedia.com/terms/i/interest.asp) per quarter is 4% (but interest is only compounded annually), then it will take 18 quarters (72 / 4) or 4.5 years to double the principal. If the population of a nation increases at the rate of 1% per month, it will double in 72 months, or six years.

## Who Came Up With the Rule of 72?

The Rule of 72 dates back to 1494, when Luca Pacioli referenced the rule in his comprehensive mathematics book _Summa de Arithmetica_. Pacioli makes no derivation or explanation of why the rule may work, so some suspect the rule predates Pacioli’s novel.

## How Do You Calculate the Rule of 72?

Here’s how the Rule of 72 works. You take the number 72 and divide it by the investment’s projected annual return. The result is the number of years, approximately, it’ll take for your money to double.

For example, if an investment promises an 8% annual compounded rate of return, it will take approximately nine years (72 / 8) to double the invested money. Note that a compound annual return of 8% is plugged into this equation as eight, and not 0.08, giving a result of nine years (and not 900).

If it takes nine years to double a $1,000 investment, then the investment will grow to $2,000 in year nine, $4,000 in year 18, $8,000 in year 27, and so on.

## What Is the Difference Between the Rule of 72 and the Rule of 73?

The Rule of 72 primarily works with interest rates or rates of return that fall in the range of 6% and 10%. When dealing with rates outside this range, the rule can be adjusted by adding or subtracting one from 72 for every three points the interest rate diverges from 8%. For example, the rate of 11% annual compounding interest is three percentage points higher than 8%. Hence, adding one to 72 leads to using the "Rule of 73" for higher precision.

For daily or [continuous compounding](https://www.investopedia.com/terms/c/continuouscompounding.asp), using 69.3 as the numerator gives a more accurate result. Some people adjust this to 69 or 70 for the sake of easy calculations.

## The Bottom Line

The Rule of 72 can also estimate how long it will take for [debt](https://www.investopedia.com/terms/d/debt.asp) to double at a fixed annual rate of return. By divide 72 by the interest rate on a loan, you can see how quickly your debt could double if you only make minimum payments. For example, a credit card with a 20% interest rate would double your debt in just 3.6 years (72 / 20).

The Rule of 72 highlights how important it is to pay off high-interest debt quickly to avoid it [spiraling](https://www.investopedia.com/articles/pf/12/the-debt-spiral.asp) out of control.

> **Article Sources**
>
> 1.  U.S. Securities and Exchange Commission. “[Creating Choices](https://www.sec.gov/investor/projectchange/creating_choices.shtml).”
>     
> 2.  Chance, via Internet Archive Wayback Machine. “[How the Rule of 72 Can Provide Guidance to Advance Your Wealth, Weight, Career, and Gas Mileage](https://web.archive.org/web/20240526173205/https://chance.amstat.org/2013/09/visualrev_26-3/).”
>     
> 3.  Mathematical Association of America. “[Mathematical Treasures—Pacioli’s Summa](https://old.maa.org/press/periodicals/convergence/mathematical-treasures-paciolis-summa).”
>     
> 4.  University of Illinois System. “[How the Rule of 72 Can Help You Build Wealth—or Sink Deeper Into Debt](https://blogs.uofi.uillinois.edu/view/7550/446933598).”