Rule of 72 Calculator (2024)

Calculator Use

Use the Rule of 72 to estimate how long it will take to double an investment at a given interest rate. Divide 72 by the interest rate to see how long it will take to double your money on an investment.

Alternatively you can calculate what interest rate you need to double your investment within a certain time period. For example if you wanted to double an investment in 5 years, divide 72 by 5 to learn that you'll need to earn 14.4% interest annually on your investment for 5 years: 14.4 × 5 = 72.

The Rule of 72 is a simplified version of the more involved compound interest calculation. It is a useful rule of thumb for estimating the doubling of an investment. This calculator provides both the Rule of 72 estimate as well as the precise answer resulting from the formal compound interest calculation.

Interest Rate
The annual nominal interest rate of your investment in percent.
Time Period in Years
The number of years the sum of money will remain invested. You can also input months or any period of time as long as the interest rate you input is compounded at the same frequency.
Compounding
This calculator assumes the frequency of compounding is once per period. It also assumes that accrued interest is compounded over time.

Rule of 72 Formula

The Rule of 72 is a simple way to estimate a compound interest calculation for doubling an investment. The formula is interest rate multiplied by the number of time periods = 72:

R * t = 72

where

  • R = interest rate per period as a percentage
  • t = number of periods

Commonly, periods are years so R is the interest rate per year and t is the number of years. You can calculate the number of years to double your investment at some known interest rate by solving for t: t = 72 ÷ R. You can also calculate the interest rate required to double your money within a known time frame by solving for R: R = 72 ÷ t.

Derivation of the Rule of 72 Formula

The basic compound interest formula is:

A = P(1 + r)t,

where A is the accrued amount, P is the principal investment, r is the interest rate per period in decimal form, and t is the number of periods. If we change this formula to show that the accrued amount is twice the principal investment, P, then we have A = 2P. Rewriting the formula:

2P = P(1 + r)t , and dividing by P on both sides gives us

(1 + r)t = 2

We can solve this equation for t by taking the natural log, ln(), of both sides,

\( t \times ln(1+r)=ln(2) \)

and isolating t on the left:

\( t = \dfrac{ln(2)}{ln(1+r)} \)

We can rewrite this to an equivalent form:

\( t = \dfrac{ln(2)}{r}\times\dfrac{r}{ln(1+r)} \)

Solving ln(2) = 0.69 rounded to 2 decimal places and solving the second term for 8% (r=0.08):*

\( t = \dfrac{0.69}{r}\times\dfrac{0.08}{ln(1.08)}=\dfrac{0.69}{r}(1.0395) \)

Solving this equation for r times t:

\( rt=0.69\times1.0395\approx0.72 \)

Finally, multiply both sides by 100 to put the decimal rate r into the percentage rate R:

R*t = 72

*8% is used as a common average and makes this formula most accurate for interest rates from 6% to 10%.

Example Calculations in Years

If you invest a sum of money at 6% interest per year, how long will it take you to double your investment?

t=72/R = 72/6 = 12 years

What interest rate do you need to double your money in 10 years?

R = 72/t = 72/10 = 7.2%

Example Calculation in Months

If you invest a sum of money at 0.5% interest per month, how long will it take you to double your investment?

t=72/R = 72/0.5 = 144 months(since R is a monthly rate the answer is in months rather than years)

144 months = 144 months / 12 months per years = 12 years

References

Vaaler, Leslie Jane Federer; Daniel, James W. Mathematical Interest Theory (Second Edition), Washington DC: The Mathematical Association of America, 2009, page 75.

Weisstein, Eric W. "Rule of 72." From MathWorld--A Wolfram Web Resource, Rule of 72.

Rule of 72 Calculator (2024)

FAQs

Which answer is the correct calculation for the Rule of 72? ›

Here's how it works: Divide 72 by your expected annual interest rate (as a percentage, not a decimal). The answer is roughly the number of years it will take for your money to double. For example, if your investment earns 4 percent a year, it would take about 72 / 4 = 18 years to double.

Why is the Rule of 72 useful if the answer will not be exact? ›

The rule of 72 can help you get a rough estimate of how long it will take you to double your money at a fixed annual interest rate. If you have an average rate of return and a current balance, you can project how long your investments will take to double.

Does the Rule of 72 actually work? ›

How the Rule of 72 Works. For example, the Rule of 72 states that $1 invested at an annual fixed interest rate of 10% would take 7.2 years ((72 ÷ 10) = 7.2) to grow to $2. In reality, a 10% investment will take 7.3 years to double (1.107.3 = 2). The Rule of 72 is reasonably accurate for low rates of return.

How do you solve the Rule of 72? ›

Do you know the Rule of 72? It's an easy way to calculate just how long it's going to take for your money to double. Just take the number 72 and divide it by the interest rate you hope to earn. That number gives you the approximate number of years it will take for your investment to double.

How to double your money in 3 years? ›

The classic approach to doubling your money is investing in a diversified portfolio of stocks and bonds, which is likely the best option for most investors. Investing to double your money can be done safely over several years, but there's a greater risk of losing most or all your money when you're impatient.

How can I double $5000 dollars? ›

How can I double $5000 dollars? One way to potentially double $5,000 is by investing it in a 401(k) account, especially if your employer matches your contributions. For example, if you invest $5,000 and your employer offers to fully match at 100%, you could start with a total of $10,000 in your account.

What are the flaws of the rule of 72? ›

The problem with applying the rule of 72 is that these types of fixed income investments offer a guaranteed rate of return for only a specified period, Briggs notes. A CD with a 6.0% rate may mature after only one year, for example, and that's much shorter than the 12 years it will take to double in value.

What will double my money in 10 years? ›

The formula for the rule of 72

This being a formula, it works in the opposite direction, too: You can figure the compound rate of return required to double your money in a certain time frame. For instance, to double your money in 10 years, the compound rate of return would have to be 7.2%.

Does rule of 72 apply to 401k? ›

Rule 72(t) allows for penalty-free withdrawals from individual retirement accounts (IRAs) and other tax-advantaged retirement accounts like 401(k)s and 403(b) plans. It is issued by the Internal Revenue Service (IRS).

How long does it take to double my 401k? ›

Your investments

With an annual 4% return, it would take 18 years (72/4) to approximately double. With a 6% return, it would take 12 years (72/6), while with an 8% return it would take 9 years (72/8).

How long will it take to double a $2000 investment at 10% interest? ›

However, the more precise method to calculate the exact number of years is using the exact doubling time which is 7.27 years, based on compound interest. Therefore, the correct answer to the question of how long it will take to double a $2,000 investement at 10% interest is A. 7.27 years.

What are three things the Rule of 72 can determine? ›

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.

What is the $1 rule? ›

The $1 rule is simple: If something will cost $1 or less per use, it's okay to buy. A $10 item should get at least 10 uses. A $100 item should get 100 uses, and so on.

How many years does it take to double your money? ›

Very few investors know how long it takes to double their money. Rule of 72 can be of help. Divide 72 by the expected rate of return and the answer is the number of years required to double your money. For example, if a bond offers 6 percent rate of interest per year, then you will double your money in 12 years.

What should be kept in mind when using the rule of 72 formula? ›

You divide 72 by your expected annual rate of return. This calculation will help you arrive at the approximate number of years it'll take for your investment to double. Consider this example: 5% Rate of Return: If you're anticipating an average return of 5% on an investment, you'd divide this return into 72.

What is the Rule of 72 used to calculate quizlet? ›

The number of years it takes for a certain amount to double in value is equal to 72 divided by its annual rate of interest.

Which one of these formulas correctly defines the Rule of 72? ›

The 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. To calculate the time period an investment will double, divide the integer 72 by the expected rate of return.

What is the formula for the Rule of 72 is blank? ›

The rule is this: 72 divided by the interest rate number equals the number of years for the investment to double in size. For example, if the interest rate is 12%, you would divide 72 by 12 to get 6. This means that the investment will take about 6 years to double with a 12% fixed annual interest rate.

What is the Rule of 72 chegg? ›

how long it will take for your investment to double in value. Simply divide the number 72 by your investment's expected rate of return (interest rate). Assuming an expected rate of return of 9%, your investment will double in value about every 8 years ( 72 divided by 9 equals 8 ).

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