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. 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 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. If you have a little more time and want a more accurate result, you can use the following logarithmic formula:. Here's how the logarithmic formula looks in this case:.
If you use the logarithmic formula, the answer is 8. But if you run the numbers using the logarithmic formula, you get 35 years—a difference of an entire year. The Rule of 72 works best over long periods of time. 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.
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. 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.
The earliest known reference to the Rule of 72 comes from Luca Pacioli's book, "Summa de Arithmetica. 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. Use this same formula to figure out the return on other investments by diving 72 with the expected annual rate of return.
Stanford University. Table of Contents Expand. Table of Contents. What Is the Rule of 72? For continuous compounding, 69 gives accurate results for any rate, since ln 2 is about Since daily compounding is close enough to continuous compounding, for most purposes 69, For lower annual rates than those above, Note: The most accurate value on each row is in italics, and the most accurate of the simpler rules in bold.
An early reference to the rule is in the Summa de arithmetica Venice, He presents the rule in a discussion regarding the estimation of the doubling time of an investment, but does not derive or explain the rule, and it is thus assumed that the rule predates Pacioli by some time. In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, keep as a rule [the number] 72 in mind, which you will always divide by the interest, and what results, in that many years it will be doubled.
Example: When the interest is 6 percent per year, I say that one divides 72 by 6; 12 results, and in 12 years the capital will be doubled. For higher rates, a larger numerator would be better e. The Eckart—McHale second-order rule the E-M rule provides a multiplicative correction for the rule of To compute the E-M approximation, multiply the rule of As the actual doubling time at this rate is 4.
To obtain a similar correction for the rule of 70 or 72, one of the numerators can be set and the other adjusted to keep their product approximately the same. The E-M rule could thus be written also as. For periodic compounding , future value is given by:. This approximation increases in accuracy as the compounding of interest becomes continuous see derivation below. Alternatively, the E-M rule is obtained if the second-order Taylor approximation is used directly.
For continuous compounding , the derivation is simpler and yields a more accurate rule:. From Wikipedia, the free encyclopedia. Not to be confused with year rule. Methods of estimating the doubling time of an investment.
For example PPF interest rate is now 7. The easiest way to do this is to figure out how long each investment instrument takes to double your money. It would be easier to choose a scheme until you know which one will double your money the earliest. Let's glance at Rule 72 using a bank FD as an example.
As a result, if the interest rate on that particular bank FD remains constant for the next 12 years, you will have doubled your money. You can also use this rule in reverse to figure out how much interest rate you'll need to double your money in a particular period. For instance, suppose you want to double your money in three years. To double your money in three years, you'll need a 24 percent interest rate. Now let's apply Rule 72 to different investment vehicles to calculate how much time it will take to double your investments.
If the interest rate remains constant, it will take approximately 9. In ten years and four months, KVP promises to nearly double your investment. At the present interest rate of 6. If the rate stays unchanged in the future, it will take Rule 72 does not have a precise figure, but it does ensure that one has a rough estimate of his or her investment objective and the time required to achieve it.
The thumb rule is typically applied to fixed-rate investments rather than volatile asset categories such as stocks, mutual funds, and so on. For Quick Alerts. What if you could plug some numbers into a simple formula and find out how long it would take for your investments to double?
That's exactly what the Rule of 72 does. Here's what you need to know about how it works and why it's a key tool to keep in your investing toolbox. The Rule of 72 is a mathematical principle that estimates the time it will take for an investment to double in value. The mention of math might make your jaw clench, but the Rule of 72 is actually a very basic formula that anyone can use.
However, you can only apply this rule to compounding growth or decay. In other words, you can only use it for investments that earn compound interest , not simple interest. With simple interest, you only earn interest on the principal amount you invest. Compound interest is "interest earned on interest": It accrues on accumulated interest, in addition to the principal.
Because interest is essentially being added into your principal, and used as the base for fresh interest calculations, compounding makes your investment grow exponentially. Meaning: As interest accrues and the quantity of money increases, the rate of growth becomes faster.
It doesn't have to be investment interest; anything that augments your principal creates "the magic of compounding. Therefore, the Rule of 72 applies. On the other hand, if you choose to withdraw your dividends rather than reinvest them, your earnings might not compound, and the Rule of 72 wouldn't work. To calculate the Rule of 72, all you have to do is divide the number 72 by the rate of return. You can use the formula below to calculate the doubling time in days, months, or years, depending on how the interest rate is expressed.
For example, if you input the annualized interest rate, you'll get the number of years it will take for your investments to double. While usually used to estimate the doubling time on a growing investment, the Rule of 72 can also be used to estimate halving time on something that's depreciating. The formula works exactly the same either way - simply plug in the inflation rate instead of the rate of return, and you'll get an estimate for how many years it will take for the initial amount to lose half its value.
To calculate the doubling time using the Rule of 72, you'd input the numbers into the formula as follows:. All of this is also assuming you're not adding to your initial investment over time, which makes the fact that your money is doubled in less than a decade all the more impressive. The number 72 is a good estimator in most situations and, thanks to it being an easily divisible number, it makes for simple math.
Most investment accounts, including retirement accounts, brokerage accounts, index funds, and mutual funds fall into this range of return. But with a different range, you might want to fiddle a bit - same formula, but different numbers to divide by.
What Is the Rule of 72? The Rule of 72 is. The Rule of 72 is a quick, useful formula that is popularly used to estimate the number of years required to double the invested money at a given annual. The Rule of 72 is a calculation that estimates the number of years it takes to double your money at a specified rate of return.