Rule of 72 Calculator

Calculate the time or rate needed to double an investment using the rule of 72.

Calculate the time needed to double an investment with a specified rate of return.

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Calculate the rate of return needed to double an investment in the specified time.

years

Estimated Time:

13.091 yrs
The result above is an estimate using the rule of 72 formula. The actual time is 12.946 yrs

Growth Over Time

This calculation is based on widely-accepted formulas, but it is not a recommendation for how to handle your finances. Consult with a financial professional before making financial decisions.
Learn how we calculated this below


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How to Calculate the Time to Double an Investment

The world of finance can be confusing for people, if not outright intimidating. To think critically about their finances, the average person needs simple rules of thumb or shortcut calculations.

They may not produce exact results, but they are a starting point for meaningful analysis. One of the more useful rules of thumb for saving and investing is the “Rule of 72” – a simple calculation to determine how much time it takes for your money to double in value based on compound interest.[1]

The Significance of Compound Interest

As the great Albert Einstein once said, “the power of compound interest is the most powerful force in the universe” and “the greatest mathematical discovery of all time.”[2]

Consider the example of a doubling penny. If a penny were able to double its value every day, it would be worth around $5 million at the end of 30 days.[3] That’s the the power of compound interest.

The “power” of compounding returns (the money earned on your investments) is that your money not only earns a return on the principle, but it also earns money on the returns. Time is what makes compounding returns work so well. Over time, the compounding effect becomes exponential and your investment grows significantly.

Time and compounding returns can turn even the smallest amounts of money into significant savings. Want to know how much? You can use the Rule of 72 to calculate how fast your savings accumulate.[4]

Rule of 72 Formula

The Rule of 72 is a straightforward, easy-to-remember formula you can use at any time to calculate how long it will take your money to double.

The Rule of 72 formula is:

years \times rate = 72

The time it will take to double an investment in years times the interest rate is equal to 72.

How to Find the Number of Years for an Investment to Double

You have $1000 in savings earning 3% annually, and you want to know how long it will take to grow to $2,000.

By switching the formula around, you can solve for the time it takes to double using the Rule of 72.

years = \frac{72}{rate}

Substitute the interest rate in the formula to calculate the time to double.

\frac{72}{3\%} = 24\ years

You can see that if you target a higher rate of return of 6% by investing in the stock market, the doubling time is less:

\frac{72}{6\%} = 12\ years

How to Find the Rate Needed to Double an Investment

For investors wanting to determine the rate of return they need to double their money in, say, ten years, they would change the formula as follows:

rate = \frac{72}{years}

For example, an investor wanting to double his $50,000 investment to $100,000 in 10 years would need to earn a rate of return of 7.2%.

\frac{72}{10} = 7.2\%

How to Use the Rule of 72 — Some Examples

The Rule of 72 has a number of useful applications where you can calculate growth at a compounded rate.

For example, if you want to estimate how long it would take for the gross national product (GDP) to double, divide 72 by the annual rate. If the GDP is growing at 3%, the economy could be expected to double in 24 years (72 ÷ 3 = 24 years).

Another practical application is determining the point at which inflation will cut your purchasing power by half. If inflation is 7%, it will cut your purchasing power in half in just over ten years (72 ÷ 7 = 10.3).

You can also use it to see how a credit balance might grow based on certain interest rates. If you are paying 14% interest on a credit card (or any other type of loan charging compound interest), the amount you owe will double in about five years. Or, at 6% inflation, an investment will lose half its value in 12 years. (72 ÷ 6 = 12).

The Rule of 72 is also helpful if you’re looking to double the value of an investment and want to know how many years it will take or the rate of return required. For example, the number of years it will take to double a $20,000 investment at a 10% return would be 7.2 years (72 ÷ 10 = 7.2).

To solve for the rate of return needed to double your investment in 12 years, it’s 72 ÷ 12 = 6%.

You can also use it to calculate the rate of return on an investment that has already doubled in value. For example, if XYZ company stock doubled in value over the last eight years, you calculate the growth rate by dividing 72 ÷ 8, which means it grew at 9% annually.

Is the Rule of 72 Precise?

The Rule of 72 has never been touted as a precise calculation. At best, it’s an approximation, although it is more accurate when using lower rates of return than larger ones.

The Rule of 72 works best with return rates ranging from 6% to 10%, with 8% as the median. For every three percentage points above 8%, you would add 1 to 72.

For example, a compounding rate of 11% would use the Rule of 73 to calculate the doubling time.

For rates below the 8% threshold, you would subtract 1 from 72. For example, the Rule of 71 would apply to a 5% compounding rate (3 percentage points below 8%).

For the most accurate doubling time calculation, you would use the Rule of 69.3%, but that could be troublesome for most people. Rounding it up to 70 would be easier; however, the Rule of 72 is used because it has more factors (2, 3, 4, 6, 12, 24, etc.).

The Rule of 69.3 more accurately calculates results at lower return rates. However, at higher return rates, it’s not as accurate.

Time for Investment to Double at Various Rates

Table showing the time it takes in years for an investment to double at various interest rates using the Rule of 72 and Rule of 69.3 formulas.
Annual Rate Actual Years Rule of 72 Rule of 69.3
1% 69.66 72 69.3
2% 35 36 34.65
3% 23.45 24 23.1
4% 17.67 18 17.33
5% 14.21 14.4 13.86
10% 7.27 7.2 6.93
20% 3.8 3.6 3.47
30% 2.64 2.4 2.31
40% 2.06 1.8 1.73
50% 1.71 1.44 1.39
75% 1.24 0.96 0.924
100% 1 0.72 0.693

Precise Time to Double Formula

There’s a more precise formula to calculate the time to double. While it’s not as convenient, it is much more accurate than the rule of 72.

years = \frac{ln(2)}{ln\left(1 + rate\right)} \approx \frac{72}{rate}

While it’s best to use calculators and spreadsheet programs for more precise calculations, the Rule of 72 is ideal for quick mental math to determine approximate values.

References

  1. O'Neill, B., The Rule of 72: A Tool to Measure Small Steps to Wealth, Rutgers, May 2017, https://njaes.rutgers.edu/sshw/message/message.php?p=Finance&m=349
  2. Seagull, B., The Life-Changing Magic of Numbers, Penguin Random House UK, 2018, https://www.penguin.co.uk/books/111/1116561/the-life-changing-magic-of-numbers/9780753552803.html
  3. Ziv, S., Which Would You Pick: $1,000,000 Or A Magical Penny?, Forbes, July 30, 2019, https://www.forbes.com/sites/shaharziv/2019/07/30/can-you-correctly-answer-the-magical-penny-question/?sh=564d25111a64
  4. U.S. Securities and Exchange Commission, What is compound interest?, https://www.investor.gov/additional-resources/information/youth/teachers-classroom-resources/what-compound-interest