How long will it take the amount a principal to double itself with a simple interest of 10?

Have you always wanted to be able to do compound interest problems in your head? Perhaps not... but it's a very useful skill to have because it gives you a lightning fast benchmark to determine how good (or not so good) a potential investment is likely to be.

The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years.

Y   =   72 / r   and   r   =   72 / Y

where Y and r are the years and interest rate, respectively.

Compound Interest Curve

Suppose you invest $100 at a compound interest rate of 10%. The rule of 72 tells you that your money will double every seven years, approximately:

If you graph these points, you start to see the familiar compound interest curve:

Practice using the Rule of 72

It's good to practice with the rule of 72 to get an intuitive feeling for the way compound interest works. So...

Why Stop at a Double?

There's nothing sacred about doubling your money. You can also get a simple estimate for other growth factors, as this calculator shows:

Why Does the Rule of 72 Work?

If you want to know more, see this explanation of why the rule of 72 works. (Brace yourself, because it's slightly geeked out.)

The Rule of 72 is an easy way for an investor or advisor to approximate how long it will take an investment to double based on its fixed annual rate of return. Simply divide 72 by the fixed rate of return, and you’ll get a rough estimate of how long it will take for your portfolio to double in size.

The science isn’t exact, though, and you may want to use a different formula to account for rates of return that fall outside a certain range. 

Key Takeaways

• The Rule of 72 is a simple way to calculate how long it will take an investment to double based on the annualized rate of return.
• Investors can use the rule when planning for retirement, education expenses, or any other long-term financial goal.
• For more accuracy, investors can use a logarithmic formula to calculate the time for an investment to double.
• In some situations, investors might want to use the Rule of 70 instead.

What Is the Rule of 72?

The Rule of 72 is a rule of thumb that investors can use to estimate how long it will take an investment to double, assuming a fixed annual rate of return and no additional contributions.

If you want to dive even deeper, you can use the Rule of 115 to determine how long it will take to triple your investment. 

Both of these rules of thumb can help investors understand the power of compound interest. The higher the rate of return, the shorter the amount of time it will take to double or triple an investment. 

How To Use the Rule of 72 To Estimate Returns

Let’s say you have an investment balance of $100,000, and you want to know how long it will take to get it to $200,000 without adding any more funds. With an estimated annual return of 7%, you’d divide 72 by 7 to see that your investment will double every 10.29 years. 

Here’s an example of other rates of return and how the Rule of 72 affects your investment:

However, the calculation isn’t foolproof. If you have a little more time and want a more accurate result, you can use the following logarithmic formula:

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

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 use this formula for the $100,000 investment mentioned above, with a 6% rate of return, you can determine that your money will double in 11.9 years, which is close to the 12 years you'd get if you simply divided 72 by 6. 

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

T = ln(2) / ln(1+.06)

Note

If you don’t have a scientific calculator on hand, you can usually use the one on your smartphone for advanced functions. However, the basic calculation can give you a good ballpark figure if that’s all you need.

How To Use the Rule of 72 To Estimate Compound Interest

Like most equations, you can move variables around to solve for others that aren’t certain. If you’re looking back on an investment you’ve held for several years and want to know what the annual compound interest return has been; you can 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 get a 9% annual rate of return. 

Grain of Salt

The Rule of 72 is easy to calculate, but it’s not always the right approach. For starters, it requires a fixed rate of return, and while investors can use the average stock market return or other benchmarks, past performance doesn’t guarantee future results. So it’s important to do your research on expected rates of return and be conservative with your estimates.

Also, the simpler formula works best 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 simple calculation returns a time to double of eight years. If you use the logarithmic formula, the answer is 8.04 years—a negligible difference.   

In contrast, if you have a 2% rate of return, your Rule of 72 calculation returns a time to double of 36 years. But if you run the numbers using the logarithmic formula, you get 35 years—a difference of an entire year. 

As a result, if you’re looking to just get a quick idea of how long your investment will take to double, use the basic formula. But if you’re calculating the figure as part of your retirement or education savings plan, consider using the logarithmic equation to ensure that your assumptions are as accurate as possible.

Note

The Rule of 72 works best over long periods of time. If you’re nearing retirement, it may not be as helpful because short-term volatility can give your annual return rate less time to even out. 

Rule of 72 vs. 70

The Rule of 72 provides reasonably accurate estimates if your expected rate of return is between 6% and 10%. But if you’re looking at lower rates, you may consider using the Rule of 70 instead.

For example, take our previous example of a 2% return. With the simple Rule of 70 calculation, the time to double the investment is 35 years—exactly the same as the result from the logarithmic equation.

However, if you try to use it on a 10% return, the simple formula gives you seven years while the logarithmic function returns roughly 7.3 years, which has a wider discrepancy. 

As with any rule of thumb, the Rules of 72 and 70 aren’t perfect. But they can give you valuable information to help you with your long-term savings plan. Throughout this process, consider working with a financial advisor who can help you tailor an investment strategy to your situation.

Frequently Asked Questions (FAQs)

What is the Rule of 72 used for?

The Rule of 72 is a quick formula you can use to estimate the future growth of an investment. If you know the average rate of return, you can apply a simple formula to determine how long it will take to double your investment, assuming you don't put more money into it.

Who invented the Rule of 72?

The earliest known reference to the Rule of 72 comes from Luca Pacioli's 1494 book, "Summa de Arithmetica." This book went on to be used as an accounting textbook until the mid-1600s, granting Pacioli the title of the Father of Accounting.

When does money double every seven years?

To use the Rule of 72 to figure out when your money will double itself, all you need to know is the annual rate of expected return. If this is 10%, then you'll divide 72 by 10 (the expected rate of return) to get 7.2 years. Use this same formula to figure out the return on other investments by diving 72 with the expected annual rate of return.

How long will it take money to double itself if invested at 10% compounded annually?

How long will it take a certain principal to double itself?

At what time at simple interest will a sum of money trebles itself at 10%?

How long does it take to double your money with simple interest?