The Rule of 72: Definition, Applicability and How to Use It (2024)

What is the Rule of 72?

The Rule of 72 is a quick, useful formula that is popularly used to estimate the number of years it will take to double the money invested in a given yearyield. Alternatively, it can calculate the annual compound return of an investment, given how many years it will take to double the investment.

While calculators and spreadsheet programs such as Microsoft Excel have functions to accurately calculate the exact time requireddouble the money investedThe Rule of 72 is useful for master calculations to quickly measure an approximate value. For this reason, the Rule of 72 is often taught to novice investors because it is easy to understand and calculate. The Securities and Exchange Commission also cites the Rule of 72 in classroom financial literacy resources.

Key learning points

The Rule of 72 is a simplified formula that calculates how long it takes for an investment to double in value, based on its rate of return.
The Rule of 72 applies to compound interest rates and is fairly accurate for interest rates between 6% and 10%.
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 the growth of an investment.
This estimation tool can also be used to estimate how much return an investment needs to double, given an investment period.
For different situations it is often better to use line 69, line 70 or line 73.

The Rule of 72: Definition, Applicability and How to Use It (1)

The formula for line 72

The Rule of 72 can be used in two different ways to determine an expected doubling period or required rate of return.

Years to double: 72 / expected return

To calculate the period over which an investment will double, divide the integer 72 by the expected return. The formula is based on one average interest rate over the life of the investment. The results are partial because all decimals represent an additional part of a year.

How to use the rule of 72

The Rule of 72 can apply to anything that grows at a compound rate, such as population, macroeconomics, fees, or loans. Ifgross domestic product (GDP)With an annual growth rate of 4%, the economy is expected to double in 72 / 4% = 18 years.

As for the fee eating away at investment profits, the rule of 72 can be used to demonstrate the long-term effects of these costs. A mutual fund that charges 3% iannual expense allowanceswill halve the investment sum in approximately 24 years. A borrower who pays 12% interest on their credit card (or another type of loan that charges compound interest) will double the amount they owe in six years.

The rule can also be used to determine how long it takes for the value of money to halveinflation. If inflation is 6%, a given purchasing power of money will be worth half in about twelve years (72/6 = 12). If inflation falls from 6% to 4%, an investment is expected to lose half its value within 18 years instead of 12 years.

Furthermore, the rule of 72 can be applied to a variety of maturities, provided the yield is increased annually. If the interest rate is 4% quarterly (but interest is only compounded annually), then it will take (72/4) = 18 quarters or 4.5 years to double the principal. If a country's population increases by 1% per month, it will double in 72 months or six years.

Who invented the Rule of 72?

The rule of 72 dates back to 1494 when Luca Pacioli referred to the rule in his comprehensive mathematics book called Summa de Arithmetica.Pacioli offers no derivation or explanation as to why the line might work, so some suspect that the line predates Pacioli's novel.

How do you calculate the rule of 72?

This is how the Rule of 72 works. You take the number 72 and divide it by the expected annual return on the investment. The result is the approximate number of years it will take for your money to double.

For example, if an investment plan promises an annual compounded return of 8%, it will take approximately nine years (72/8 = 9) to double the money invested. Note that a compound annual return of 8% is entered into this equation as 8 and not 0.08, which gives a result of nine years (and not 900).

If it takes nine years to double a $1,000 investment, then the investment will grow to $2,000 in year 9, $4,000 in year 18, $8,000 in year 27, and so on.

How accurate is the Rule of 72?

The Rule of 72 formula provides a fairly accurate, but approximate, timeline – reflecting the fact that it is a simplification of a more complex logarithmic equation. Do the entire calculation to get the exact doubling time.

The exact formula to calculate the exact doubling time for an investment that has a compound interest rate of r% per period is:

Use the following equation to find out exactly how long it will take to double an investment that produces an 8% annual return:

T = ln(2) / ln (1 + (8/100)) = 9.006 years

As you can see, this result is very close to the estimated value obtained at (72 / 8) = 9 years.

What is the difference between Article 72 and Article 73?

The rule of 72 mainly works with interest or returns that are between 6% and 10%. For rates outside this range, the rule can be adjusted by adding or subtracting 1 from 72 for every 3 points the interest rate deviates from the 8% threshold. For example, the annual interest rate adjustment of 11% is 3 percentage points higher than 8%.

Therefore, adding 1 (for the 3 points higher than 8%) to 72 leads to using the rule of 73 for higher accuracy. For a 14% return, that would be the rule of 74 (add 2 for 6 percentage points higher), and for a 5% return, that would mean subtracting 1 (for 3 percentage points lower) to get to the rule of 71. to lead.

For example, suppose you have a very attractive investment with a return of 22%. The Rule of 72 states that the original investment will double in 3.27 years. But since (22 – 8) is 14, and (14 ÷ 3) is 4.67 ≈ 5, the modified rule must use 72 + 5 = 77 as the numerator. This gives a value of 3.5 years, which indicates that you will have to wait another quarter to double your money, compared to the result of 3.27 years obtained from the rule of 72. The period given by the logarithmic equation is 3 ,49, so the result obtained from the modified rule is more accurate.

For daily use orcontinuous composition, using 69.3 in the numerator gives a more accurate result. Some people adjust this to 69 or 70 for simple calculations.