The “Rule of 72” is based on the mathematical concept of compound interest, the way interest rates or returns multiply when earnings are reinvested.
The “Rule of 72” has been used by financial professionals, investors, and analysts for decades. Their goal is to quickly and easily get a rough estimate of when an investment is likely to double in value, without having to use a computer or calculator.
The idea is so simple that it seems trivial: The number 72 is divided by the annual rate of return one expects from an investment. The result of this division gives an approximate idea of the number of years it will take for the initial capital to double. If, for example, someone believes that an investment in the stock market can yield an average of 8% per year, then according to this rule, it will take about 9 years to see their money double. It is a quick estimate that helps the average investor get a picture of the time and power of compound interest, without complicated calculations.
The “Rule of 72” is not some mystical investor ritual. Instead, it is based on the mathematical idea of compound interest, that is, the way in which interest rates or returns multiply when profits are reinvested. Under normal compounding conditions, the exact way to calculate the doubling time is to use logarithms, through the mathematical equation t = ln(2)/ln(1+r), where r is the annual interest rate. In this mathematical context, it turns out that the logarithm of 2, which means doubling, is associated with a constant of about 0.693. When this constant is divided by the rate of return r, the quotient is an accurate value for the years required. But for the average person who wants to make a quick estimate, using the number 72 instead of 69.3 has a practical advantage. 72 has many divisors such as 2, 3, 4, 6, 8, 9, 12, so you can easily do the division in your head for several return values. 70 or 69.3 may be more mathematically correct, but 72 is more friendly for quick estimates without a computer.
This particular “rule of 72” has become popular because it can be used by anyone with compound interest, in investments, in savings, and even to estimate how high inflation rates are reducing the purchasing power of their money. If, for example, inflation is “running” at 8.6%, a quick estimate is that the value of your money will be halved in about 8.5 years.
The important thing for everyone to understand, however, is that it does not replace full financial calculations. The “rule of 72” does not take into account taxes, costs, variability in returns, or systematic contributions. It is a quick rule of thumb, not a complete, professional calculation. That is, if a product simply gives 8% per year without reinvesting profits, the behavior does not follow the same compound interest, so the estimate of the rule loses its value. The market does not give a stable return every year. In real investments, such as stock portfolios, the annual return might be 8% one year and -5% the next. The rule of 72 assumes stability and not large fluctuations.
