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The Rule of 72 is a basic equation that investors can use to estimate how long it might take for a given amount of money to double, given a specific rate of return. The formula involves dividing 72 by the interest or return rate.

For example, a $50,000 investment that’s earning roughly 9% per year could double in about eight years (72 / 9 = 8).

The Rule of 72 can be used in cases that are based on compound returns, or compound interest. As such it can also be used to calculate how long it might take to pay down a certain amount of debt, and to gauge the impact of inflation over time.

The Rule of 72, like similar shortcuts, is meant to provide a ballpark estimate that investors can use when making their financial projections. The actual time it takes for your money to double can vary, depending on numerous factors.

What Is the Rule of 72?

The Rule of 72 helps investors understand how different types of investments might figure into their investment plans. The basic formula for the rule is:

Number of years to double an investment = 72 / Expected rate of return

The expected rate of return on an investment will naturally vary over time, and will depend on the type of investment. The Rule of 72 is a way to plug in a hypothetical return rate or annual interest rate for an investment like a stock, bond, or mutual fund.

For example, consider someone who is investing online has $10,000 in an investment that may provide a possible 6% rate of return. That investment could theoretically double in about 12 years (72 / 6 = 12). So, approximately 12 years after making an initial investment, given a potential 6% annual return, the investor would have $20,000. Again, returns are effectively compounded with this formula.

Notice that when making this calculation, investors divide by 6, not 6% or 0.06. (Dividing by 0.06 would indicate 1,200 years to double the investment, an outlandishly long time.)

This shorthand allows investors to quickly compare investments and understand whether a potential rate of return will help them meet their financial goals within a desired time horizon. For example, a bond typically offers a fixed rate of return, which could be compared to the hypothetical return of an equity investment — which might be higher, but could be less reliable.

Who Came Up with the Rule of 72?

The Rule of 72 is not new. In fact, it dates back to the late 1400s, when it was referenced in a mathematics book by Luca Pacioli. The Rule itself, though, could date even further back. Albert Einstein is often credited with its invention, although it’s not his original concept.

The Formula and Calculation of the Rule of 72

The Rule of 72 is a shortened version of a logarithmic equation that involves complex functions you would need a scientific calculator to calculate. That formula looks like this:

T = ln(2) / ln(1 + r / 100)

In this equation, T equals time to double, ln is the natural log function, and r is the compounded interest rate.

This calculation is too complicated for the average investor to perform on the fly, and it turns out 72 divided by r is a close approximation that works especially well for lower rates of return. The higher the rate of return — as the rate nears 100% — the less accurate the Rule of 72 gets.

Example of the Rule of 72 Calculation

The Rule of 72 can help investors figure out helpful information. For one, it can help them compare different types of investments that offer different rates of returns.

For example, an investor has $25,000 to invest when they open an IRA, and they plan to retire in 20 years. In order to meet a certain retirement goal, that investor needs to at least double their money to $50,000 in that time period.

The same investor is considering two investment options: One offers a 3% return and one offers a 4% return. Using the Rule of 72 the investor can quickly see that at 3% the investment could double in 24 years (72 / 3 = 24), four years past their retirement date. The investment with a 4% return could double their money in 18 years (72 / 4 = 18), giving them two years of leeway before they retire.

The investor can see that when choosing between the two options, the 4% rate of return may help them reach their financial goals, while the 3% return might leave them short.

Applying the Rule of 72 in Investment Planning

There are numerous instances in which the Rule of 72 can be applied to investment planning. But it’s also important to understand a bit about how simple and compound growth occur, and how they can come into play when using the Rule of 72 to make projections.

Simple growth, like simple interest, is when the rate of return applies only to the principal amount. A $1,000 investment that earns a 5% simple rate of return would earn $50 per year.

Compound growth is more common for long-term investments; this is when the rate of return applies to the principal investment plus all earnings from previous periods. In other words, an investor earns a return on their returns.

Example of Compound Returns

To get an idea of the power of compound interest it might help to explore a compound interest calculator, which allows users to input principal, the rate or return or interest rate, and the compounding period.

For example, imagine that an individual invests that same $1,000 at a 5% rate for 10 years with the gains compounding monthly. At the end of the investment period, they will have made more than $674, without making any additional investments.

That fact is important to consider when conceptualizing the Rule of 72, because compound interest plays a big role in helping an investment double in value within a given time frame. Here, the Rule of 72 indicates that the investor’s initial $1,000 would double in about 14.4 years (72 / 5 = 14.4 ).

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Practical Uses in Financial Projections

Higher returns are often correlated with higher risk. So the Rule of 72 can help investors gauge whether their risk tolerance — or their expected return on investment — is high enough to get them to their goal, without undue risk exposure. Depending on what their time horizon is, investors can evaluate whether they need to bump up their risk tolerance and choose investments that may offer higher returns.

By the same token, this rule can help investors understand if their time horizon is long enough at a certain rate of return. For example, the investor in the above example is already invested in the instrument that offers 3%.

The Rule of 72 can indicate that they may need to rethink their timeline for when they will retire, pushing it past 20 years. Alternatively, for those interested in self-directed investing, they could sell their current investments and buy a new investment that might offer a higher rate of return.

It’s also important to understand that the Rule of 72 does not take into account additional savings that may be made to the principal investment. So if it becomes clear that the goal won’t be met at the current savings rate, an investor will be able to consider how much extra money to set aside to help reach the goal.

Estimating Investment Doubling Times

Using the Rule of 72 to estimate investment doubling times can be a little tricky, and perhaps inaccurate, unless an investor has a clear idea of what the expected rate of return for an investment will be. For instance, it may be very difficult to get an idea of an expected return for a particularly volatile stock. As such, investors may want to proceed with caution when using it to calculate investment doubling times.

Application in Stock Market Investments

As mentioned, stock market returns can’t be predicted. But an investor could use the historic rate of return for the S&P 500 to try and get a sense of an expected return for the market at large – which can help when applying the Rule of 72 to index funds or other broad investments.

By contrast, bonds typically offer a fixed rate of return, making it easier to use the Rule of 72 effectively.

For example, if a traditional IRA, Roth IRA, or 401(k) plan includes investments that offer a potential 6% return, the investment will double in 12 years. Again, that’s an estimate, but it gives investors a ballpark figure to work with.

Use During Periods of Inflation

Money loses value during bouts of inflation, which means that the Rule of 72 can be used to determine how long it’ll take a dollar’s value to fall by half — the opposite of doubling in value. If inflation holds steady at 5%, the purchasing power of a dollar will be cut in half in about 14.4 years.

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Accuracy and Limitations of the Rule of 72

The Rule of 72 has its place in the investing lexicon, but there are some things about its accuracy and overall limitations to take into consideration.

Is the Rule of 72 Accurate?

Perhaps the most important thing to keep in mind about the Rule of 72’s accuracy is that it’s a derivation of a larger, more complex operation, and therefore, is something of an estimate. It’s not perfectly accurate, but will get you more of a ballpark figure that can help you make investing decisions.

Situations Where the Rule is Most Accurate

The Rule of 72 is only an approximation and depending on what you’re trying to understand there are a few variations of the rule that can make this estimate more accurate.

The rule of 72 is most accurate at 8%, and beyond that at a range between 6% and 10%. You can, however, adjust the rule to make it more accurate outside the 6% to 10% window.

The general rule to make the calculation more accurate is to adjust the rule by one for every three points the interest rate differs from 8% in either direction. So, for an interest rate of 11%, individuals should adjust from 72 to 73. In the other direction, if the interest rate is 5%, individuals should adjust 72 to 71.

Comparisons and Variations on the Rule

There are a few alternatives or variations of the Rule of 72, too, such as the Rule of 73, Rule of 69.3, and Rule of 69.

Rule of 72 vs. Rule of 73

The basic difference between the Rule of 72 and the Rule of 73 is that it’s used to estimate the time it takes for an investment’s value to double if the rate of return is above 10%. The Rule of 73 is only a slight tweak to the rule of 72, using different figures in the calculation.

Rules of 72, 69.3, and 69

Similarly to the Rule of 73, some people prefer to use the Rule of 69.3, especially when interest compounds daily, to get a more accurate result. That number is derived from the complete equation ln(2) / ln(1 + r / 100). When plugged into a calculator by itself, ln(2) results in a number that’s approximately 0.693147.

The Takeaway

The Rule of 72 is one of a few simple formulas investors can use to evaluate when a given investment might double in value. The advantage of these formulas is that they can be applied quickly, without using a calculator. And because the Rule of 72 generally can apply to any situation that involves the compounding of returns, interest, or inflation, investors can use it in various circumstances.

That said, it’s important to be aware that the Rule of 72 is just an estimate. It cannot control for real-world conditions that may impact risk and returns.

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FAQ

What are the flaws in the Rule of 72?

There are a few key drawbacks to using the Rule of 72, including the fact that it’s mostly accurate only for a certain subset of investments, it’s only an estimate, and unforeseen factors can cause the rate of return for an investment to change, rendering it useless.

Does the Rule of 72 apply to debt?

Yes, the Rule of 72 can be applied to debt, and it can be used to calculate an estimate of how long it would take a debt balance to double if it’s not paid down or off.

Who created the Rule of 72?

Albert Einstein often gets credit for creating this formula, but Italian mathematician Luca Pacioli most likely invented, or introduced, the Rule of 72 in the late 1400s.