In finance, rule of 72 is an important approximation rule that is used to quickly estimate the number of years it will take for an investment double in value at a given interest rate.

According to this rule, the interest rate multiplied by the number of years it will take for the investment to double is equal to 72 approximately. The rule of 72 considers exponential growth, i.e., continuous compounding.

Let’s see how it can be used in different scenarios.

Estimate the time it takes to double the investment

Let’s say you have $10,000 to invest. If you invest this money in a financial asset that provides 10% interest, then how much time will it take to double this investment. If the interest rate is represented by r and time by t, then:

r*t = 72

In our case r is 10%, so t = 72/10 = 7.2 years

According to the rule of 72, our investment of $10,000 will take 7.2 years to become $20,000 if invested at an interest rate of 10%.

To test this formula, let’s use the exponential growth formula to see how much time it will actually take to reach $20,000.

10,000*(1+0.10)^t = 20,000

If we use t as 7.2, the investment will grow to 19,862. This is quite a close estimate. The actual time it will take for our investment to become $20,000 is 7.27 years. By seeing these numbers we can say that the rule of 72 provides quite satisfactory answer for a quick calculation.

Estimating interest rate for investment

An alternative use of this formula is when you have a certain timeframe in which you want your money to double and you want to find out the interest rate at which you should invest to reach your goal. So you want your money to double in 5 years. In this case the rate at which your money should grow will be:

r = 72/5 = 14.4%

Estimate the time to decay

We can also use the rule of 72 to find out how much time your money will take to become half in value, such as in case of inflation. Let’s say the inflation rate is 7%. How much time will it take for $1,000 to become $500 in value?

7*t=72, or t = 10.28 years.

Estimating doubling time for higher interest rates

If you want to determine the doubling time when the interest rates are high, them the number 72 needs to be adjusted by adding 1 for every 3% greater than 8.

So, the formula will be:

t*r = 72+(r-8)/3

If interest rates were 26%, then time to double will be:

t = (72+(26-8)/3)/26 = 2.88

This adjustment gives a better estimate of the doubling time.