They say the number seven is a magic number and in the world of finance, there is some truth to this common saying. At least, that is, when the number two follows the seven, as in the “rule of 72.” This rule is often used to quickly determine how fast an investment will double in value and it can also be used to illustrate how much faster an investment will grow over time at different rates of return.
How Does the Rule of 72 Work?:
With the rule of 72, you simply divide your annual rate of investment return into the number 72 to arrive at an approximate number of years that it will take a lump- sum investment to double in value. For example, an investment that earns 6% per year would therefore take approximately 12 years to double (72 divided by 6 = 12) while an investment that earns 12% per year would take approximately 6 years to double (72 divided by 12 = 6). Over a period of time, differences like this can really add up, as the table below indicates:
Initial investment: $10,000
Rate of return Number of Years Value
6% 12 $20,000
6% 24 $40,000
So, at 6%, a $10,000 investment will double in 12 years and then double again in 24 years, growing to $40,000 in value.
Now, what if you could earn 12% on the same size investment:
Initial Investment: $10,000
Rate of return Number of Years Value
12% 6 $20,000
12% 12 $40,000
12% 18 $80,000
12% 24 $160,000
So, as this illustration shows, the same investment of $10,000 would increase in value to $160,000 at 12%. It would double, then double again, then double again, and then double a fourth time, resulting in vale 16 times greater than the initial investment.
Are There Limits to This Rule?:
Yes, the rule of 72 is a limited concept. The most obvious limitation is that the rule provides only an approximation. It is not intended to be precise and the calculation becomes less and less accurate as the years grow longer and the returns are greater. Taking the above examples and doing the actual math, the $10,000 investment that earns 6% would grow to exactly $40,489.35 in 24 years while the 12% return on the same $10,000 would grow to $151,786.30.
Another limitation of this rule is the fact of taxation. We know that any investment gain, once realized, is going to be taxable and the rate varies by person. Factor in taxes and the time to double will take longer.
In Summary:
Financial calculations can get complicated but the Rule of 72 is one easy way to approximate the time it will take for an investment to double in value. It is simple enough to calculate in your head and the solution provides a good approximation of future value. The rule isn’t perfect and it loses more accuracy over time, but it is still an easy, useful means to compare investment returns and predict future values.
Copyright 2012, Bryan Carey
