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The 72 Rule – The Secret to Doubling Your Assets

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72法则(72 rule)——资产翻倍的秘密

This article will introduce the content, principle and application of the Rule of 72, so that you can quickly calculate the time to double your assets.

What is the 72 rule?

The Rule of 72 is a quick formula for estimating the number of years it would take to double your invested capital at an expected average annual rate of return.

For example, when the expected annual rate of return is 8%, divide 8 by 72 to get 9, then it will take about 9 years to double the principal with an average annual rate of return of 8%.

Why 72? What is the principle of the rule of 72?

It’s actually a simple math problem.

Let the average annual rate of return be R%, after N years, the principal will double, then the relationship between R and N is:


Obviously, N=ln2/ln(1+R/100)

Now, instead of finding the specific value, we use the estimation method to calculate N.

ln2 is approximately equal to 0.69, and the equivalent infinitesimal of ln(1+R/100) is R/100, so

N is approximately equal to 69/R

Why 72 and not 69?

Because 72=2*2*2*3*3, it is a multiple of 2, 3, 4, 6, 8, 9, 12, 18, 24, 36. The probability of getting an integer with 72 will be very large, which is convenient for us to estimate.

Mathematical studies have shown that it is relatively accurate for returns between 6% and 10%.

For different situations, it may be better to also use the rule of 69, the rule of 70, or the rule of 73.

In fact, because it is an estimate, you can take any number between 69 and 73, as long as the calculation is convenient.

For example, if the rate of return is 7%, then obviously dividing 70 by 7 is very convenient to get the answer of 10 years.

It’s worth noting that the expected return on the Rule of 72 is compounded, as can be seen from the calculations above.

What is compound interest? What is the difference between compound interest and simple interest?

Application of the 72 rule

From the calculation process we found that the rule of 72 can be applied to anything that grows at a compounding rate, such as population, macroeconomic numbers, fees or loans.

If Gross Domestic Product (GDP) grows at 4% per year, the economy is expected to double in 72/4% = 18 years.

Regarding fees that cannibalise investment returns, the rule of 72 can be used to demonstrate the long-term impact of these fees. A mutual fund that charges 3% a year will halve the principal invested in about 24 years.

The 72 Rule - The Secret to Doubling Your Assets

A borrower paying 12% interest on a credit card (or any other form of loan that charges compound interest) will double the amount they owe in 6 years.

This rule can also be used to calculate how long it takes for a currency to halve due to inflation. If the inflation rate is 6%, then the currency of a certain purchasing power will be halved in value in about 12 years (72/6=12). If inflation were to drop from 6% to 4%, an investment would lose half its value in 18 years, not 12 years.

Also, the Rule of 72 can be applied to a variety of tenors as long as the rate of return is compounded annually. If the quarterly interest is 4% (but the interest is only compounded annually), it would take (72/4) = 18 quarters or 4.5 years to double the principal.

If a country’s population grows at 1% per month, it will double in 72 months, or six years.

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

Question about accuracy

If you’re after very precise timing then direct calculation is better, otherwise estimation is more convenient.

Modern computers can easily figure it out for the formula N=ln2/ln(1+R/100).


The Rule of 72 is a very simple and convenient formula for quick calculations. It has a very convenient application on the exponential growth doubling problem. It is hoped that the majority of investors will no longer have any doubts about the time issue of asset doubling through this tool.

Reference: investopedia

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