# Rule of 72 – Definition

### Rule of 72 Definition

It is a simple calculation method to estimate an investment’s doubling time with a specific fixed annual interest rate. It is the easiest and fastest way to calculate how long an investment will take to double, given a fixed annual rate of interest.

The formula for calculating the time is,

The estimated number of years needed for doubling the investment = 72 / compound interest rate.

The same formula can be used for estimating the annual rate of interest needed for doubling an amount within a specific time period.

The estimated compound rate of interest needed for doubling the money = 72 / Number of years.

### A Little More on the Rule of 72

Compound interest means, earning interest on interest. If you get 10% interest a year, then your investment of \$100 will become \$110 in one year and then in next year, your interest will be calculated on the principal amount of \$110 and so on.

Three main elements are there that impacts the growth:
• the rate of interest,
• how frequently it is to be compounded, and
• how long the account is allowed to compound.

The Rule of 72 uses the concept of natural logarithms. The logarithm is the opposite concept of power. The natural logarithm can be explained as the amount of time needed to reach a certain level of growth with continuous compounding.

The Rule of 72 gives a rough estimate rather than the exact figure. The formula is useful for doing a mental math to estimate the time. For doing this calculation, one needs to figure out the compound interest rate and put it as a whole number and not as a decimal.

For example, if someone invests \$1 at an annual compound interest rate of 10%, according to Rule of 72 the estimated number of years it will take to become \$2 is,
72 / 10 = 7.2 years.

However, in reality, it will take 7.3 years to get double. The following table provides the details of how the estimate of Rule of 72 differs from the accurate figure. In general, the Rule of 72 is almost accurate for the interest rates that fall between 6% and 10%. For other interest rates, the rule can be adjusted by adding or subtracting 1 from 72 for every 3 points the rate of interest diverges from 8%.

Some people also use the rule of 69.3 to get a more accurate result for continuous compounding. For the sake of simplicity, some may also substitute it with 69.

However, 72 is a convenient number as it has the small divisors like 1, 2, 3, 4, 6, 8 and 9. It makes the calculation simple and easy.

### Academic Research on Rule of 72

• ·       Derivation and accuracy of the ‘rule of 72, Blatner, K. A., & Cross, W. M. (1989). International Journal of Mathematical Education in Science and Technology20(5), 723-729. By making use of Rule 72, this research thesis made it clear that for an investment having an annually compounded interest, the time taken for this interest to double can be estimated using this rule. This paper described the deviation and evaluation of this rule and also explains when it can be applied. This paper was passed under the Agriculture Research Center at Washington State University.
• The Rule Of 72?, Spitzer, J., & Singh, S. (1999). Journal of Financial Counseling and Planning10(1). This paper explains the real and key interest of the Rile 72 and why it can be applied to solving economic issues.
• The Rule of 72: Why It Works, Morris, R. L., & Lerro, A. J. (1995). Journal of Financial Education, 55-57. Some scholars in the time past have asked themselves why rule 72 works with no concrete theory to support their claims. This paper, however, explains the main interest and reason why rule 72 till date is still reliable and effective in solving economic issues.
• A note on the rule of 72 or how long it takes to double your money, Sandler, L. (1973).  Investment Analysts Journal2(3), 34-34. According to previous research, the main work of Rule 72 is to double your money/investment. So, this research paper gives a comprehensive note on the time it takes your investment to be doubled with the help of rule 72.
• A technical fix for the rule of 72… or is it the rule of 69?, Cuddington, J. T. (2002). Journal of Financial Service Professionals56(6), 36. This research paper explains the technical adjustments made to rule 72. This study helps to reveal the true nature of rule 72 and how it can be used to correct the economic problem.
• The Rule of 72 for Lifetime Savings, Thomas, P. (2010). According to the results gotten from this paper, the importance of tutoring young investors on the importance of saving for retirement from a very tender age was explained quoting from the beliefs of Rule 72. Note that if an investor invest a certain amount of money at the beginning of a year, over the course of his working life at a constant interest rate of a known % per year, an approximate value that indicates half of the terminal value of his account can be defined based on first 72/r years of contribution.
• The “Rule of 72” is a simple rule of thumb often utilized by ﬁnancial analysts to estimate the doubling time of money. The rule states that the time to double in …, MATTHEW, J.  This research paper believes Rule 72 is a simple rule of thumb that is often used by financial analysts to evaluate and estimate the rate at which an investment can be doubled. This study explains the way and manner in which this rule (Rule 72) adopts in the doubling of your investments.
• rule of 70′: extending ‘rule of 72‘arguments to interest rates with quarterly, monthly, and daily compounding, Cross, W. M., & Blatner, K. A. (1991). International Journal of Mathematical Education in Science and Technology22(2), 167-176. Although, the rule 72 can be mathematically induced depending, on the manner of approach. This paper, however, explains the methods adopted in the process of inducing the interest rates with either monthly, quarterly of daily compounding.
• How Good is the “Rule of 72”?, Kroopnick, A. (1979). The Two-Year College Mathematics Journal10(4), 279-280. The main aim of this paper is to explain the extent to which Rule 72 is relevant. It studies the various aspects where Rule 72 can be applied in the economy.
• A simple approximation of Tobin’s q, Chung, K. H., & Pruitt, S. W. (1994). Financial management, 70-74. A simple formula that helps in the approximation of Tobin’s q was developed in the course of this research. This formula uses only the accounting and financial information to proffer answers/solutions to economic situations. A no of regression was compared with the approximate q values with those ones gotten from the Lindenberg and Ross a 1981.