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What Is the Rule of 72?

Investors may use it to figure out when their investment will double

The Rule of 72 is a simple approach for an investor or adviser to anticipate how long it will take an investment to double based on its constant yearly rate of return. Simply divide 72 by the constant rate of return, and you’ll obtain a ballpark estimate of how long it will take for your portfolio to double in size.

The science isn’t perfect, however, and you may want to use a different calculation to account for rates of return that fall outside a particular range. 

Key Takeaways

The Rule of 72 is a simple approach to determine how long it will take an investment to double based on the annualized rate of return.

Investors may utilize the rule while budgeting for retirement, college fees, or any other long-term financial objective.

For additional precision, investors may use a logarithmic formula to determine the time for an investment to double.

In certain cases, investors may prefer to apply the Rule of 70 instead.

What Is the Rule of 72?

The Rule of 72 is a rule of thumb that investors may use to predict how long it will take an investment to double, assuming a stable yearly rate of return and no further contributions.

If you want to delve any deeper, you may utilize the Rule of 115 to predict how long it will take to triple your investment. 

Both of these rules of thumb may assist investors appreciate the potential of compound interest. The greater the rate of return, the shorter the period of time it will take to double or triple an investment. 

How To Use the Rule of 72 To Estimate Returns

Let’s imagine you have an investment balance of $100,000, and you want to know how long it will take to increase it to $200,000 without adding any additional cash. With a projected yearly return of 7%, you’d divide 72 by 7 to find that your investment would double every 10.29 years. 

Here’s an illustration of alternative rates of return and how the Rule of 72 impacts your investment:

Rate of Return Years it Takes to Double
1% 72
2% 36
3% 24
4% 18
5% 14.4
6% 12
7% 10.3
8% 9
9% 8
10% 7.2
11% 6.5
12% 6

However, the computation isn’t flawless. If you have a little more time and want a more exact answer, you may use the following logarithmic formula:

T = ln(2) / ln(1+r)1 Stanford University. "EE204: Business Management forElectrical Engineers and Computer Scientists."

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

So, to utilize this technique for the $100,000 investment indicated above, with a 6% rate of return, you may figure that your money would double in 11.9 years, which is close to the 12 years you'd get if you just divided 72 by 6.

Here's how the logarithmic formula appears in this case:

T = ln(2) / ln(1+.06)
If you don’t have a scientific calculator on hand, you can typically use the one on your smartphone for complex tasks. However, the simple computation may give you a reasonable estimate value if that’s all you need.

How To Use the Rule of 72 To Estimate Compound Interest

Like most equations, you may shift variables around to solve for others that aren’t definite. If you’re looking back on an investment you’ve had for many years and want to know what the yearly compound interest return has been; you may divide 72 by the number of years it took for your investment to double.

For example, if you started out with $100,000 and eight years later the balance is $200,000, divide 72 by 8 to obtain a 9% annual rate of return.

Grain of Salt

The Rule of 72 is simple to compute, but it’s not necessarily the best strategy. For starters, it needs a set rate of return, and although investors may use the average stock market return or other benchmarks, previous success doesn’t guarantee future outcomes. So it’s crucial to perform your study on predicted rates of return and be cautious with your estimations.

Also, the simplified method works well for return rates between 6% and 10%. The Rule of 72 isn’t as accurate with rates on either side of that range.

For example, with a 9% rate of return, the straightforward computation yields a time to double of eight years. If you apply the logarithmic formula, the answer is 8.04 years—a tiny change.

In comparison, if you had a 2% rate of return, your Rule of 72 computation produces a time to double of 36 years. But if you do the calculations using the logarithmic approach, you get 35 years—a difference of one whole year.

As a consequence, if you’re seeking to only obtain a fast indication of how long your investment will take to double, apply the simple method. But if you’re calculating the amount as part of your retirement or school savings plan, consider utilizing the logarithmic equation to verify that your assumptions are as precise as possible.
The Rule of 72 works best over lengthy periods of time. If you’re approaching retirement, it may not be as useful since short-term volatility might give your yearly return rate less time to settle out.

Rule of 72 vs. 70

The Rule of 72 delivers relatively accurate predictions if your projected rate of return is between 6% and 10%. But if you’re looking at lower rates, you may try employing the Rule of 70 instead.

For example, consider our prior example of a 2% return. With the basic Rule of 70 calculation, the period to double the investment is 35 years—exactly the same as the answer from the logarithmic equation.

However, if you attempt to utilize it on a 10% return, the basic formula gives you seven years while the logarithmic function produces around 7.3 years, which has a greater gap.

As with any rule of thumb, the Rules of 72 and 70 aren’t perfect. But they may provide you crucial information to assist you with your long-term savings goal. Throughout this process, consider consulting with a financial adviser who can help you design an investing plan to your circumstances.

Frequently Asked Questions (FAQs)

What is the Rule of 72 used for?

The Rule of 72 is a fast calculation you may apply to predict the future growth of an investment. If you know the typical rate of return, you may use a simple calculation to predict how long it will take to double your investment, providing you don't put extra money into it.

Who developed the Rule of 72?

The oldest documented mention to the Rule of 72 is from Luca Pacioli's 1494 work, "Summa de Arithmetica." This book went on to be utilized as an accounting textbook until the mid-1600s, gaining Pacioli the title of the Father of Accounting.

When does money double every seven years?

To apply the Rule of 72 to find out when your money will double itself, all you need to know is the yearly rate of projected return. If this is 10%, then you'll divide 72 by 10 (the projected rate of return) to get 7.2 years. Use this similar approach to find out the return on other assets by substituting 72 with the projected annual rate of return. 

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