What is the Rule of 72?

The ‘Rule of 72’ is commonly used regarding calculations on investment returns and determining when an investment might double. What is this mysterious rule, how did it come about and how can it be used?

I will aim to answer these questions in the following sections.

Rule of 72 – What is it and how is it derived?

The Rule of 72 is a formula that is used to estimate (approximate) the number of years required to double an investment depending on the related annual rate of return (where the rate of return for that year is the net gain or loss expressed as a percentage). This final figure should exclude any costs associated with this investment such as brokerage fees and the like.

The Rule of 72 formula is as follows:

Years to double = 72 divided by rate of return on investment (%)

Where does this mysterious 72 come from? Using our high school math, we can use the following compound interest formula (we assume the amount of compounding is occurring once per year):

where:

A = amount in the future

P = amount paid at the beginning (principle)

r = interest rate per year

t = number of years

n = number of times compounded per year.

 

So, using this formula, how long will it take to double our $A to $2A.

 

Using logarithms to solve this equation, we have:

ln 2 = t ln(1 + r)

We can find the value of the right-hand side for different values of r. When we do this, we find that the values are close to 72.

Taking as an example, say if r = 8% = 0.8, then:

This means it would take around 9 years to double our money at an annual return of 8%.

Now multiplying 9 by 8 give us our mysterious 72!

For other interest rates, this calculation ranges through from 70 through to 74, however, the approximation of 72 is quite close.

 

Rule of 72 – How is it used?

Using the ‘Rule of 72’, we can derive an approximate number of years for investment to double, depending on the rate of return. See the following table:

Note: In my calculations below I have rounded up years to the nearest half year.

Rate of Return (% per annum)	Approximate time it takes for the investment to double (#years; rounded up to nearest half year)
2	36
4	18
10	7.5
15	5
20	4
30	2.5
40	2

 

 

 

The time taken to double an investment gives insight into the magical power of compounding. As revealed in Inc.com, there is a belief that Einstein called compound interest the “8th Wonder of the World.” As we can see from the above table, amazing results can be had with an investment if we continue to obtain high percentage returns, year after year.

 

Your PROFITABLE ACTION STEPS this time around:

1. Using the ‘Rule of 72’, check on your current returns on investment and see how they long they take to double
2. If you have a share portfolio that pays dividends, if you don’t already, consider having all of the dividends reinvested into more shares – this helps to compound your investment over time
3. Check out my recent article on the amazing Warren Buffett.

 

Stay safe, healthy and wise and most importantly of all, take ACTION.