What is the Rule of 72?

How would you calculate the number of years required to double your money at a given rate of return (i)? If you understand the relationship between a present value (PV) and a future value (FV), given by the expression,

rule of 72_1

For your money to double, that means FV = 2 PV, and we have the number of years (n) to be,

rule of 72_2

While it is not complicated to calculate, but you will need a calculator for this formula. That is why we have the rule of 72 to help us. 

“For any amount which is compounding periodically at a fixed growth rate, the number of periods required for that amount to double can be estimated by dividing the percentage growth rate into 72”

 

It is a quick and easy way for investors to work out how many years it would take an investment to, theoretically, double in value. It also works if you need to estimate how long it would take for a sum of money to halve in value too.

 

Let’s say an investment is expected to return 10% a year. So 72 / 10 = 7.2. It would thus take roughly seven years for the investment to double. Now let’s assume that the rate of inflation is 5%. With 72 / 5 = 14.1. Meaning fourteen years from now, your savings would have lost half its purchasing power. 

 

Comparison of rule of 72 and exact calculation as below:

Rate (%)

Rule of 72

Actual Periods

1

72

69.661

5

14.4

14.207

10

7.2

7.273

25

2.88

3.106

50

1.44

1.71

100

0.72

1

 
The Rule of 72 provides a good approximation for annual compounding, and for compounding at lower rates of returns only, generally from 4% to 15%. The approximations are less accurate at higher interest rates, as you can see from the table above. 
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