FP Article 29 (To sign up for a FREE 6-lesson eCourse on Defeating Credit Card Debt, please click here.)

What is the Rule of 72?

by Rajen Devadason

Most people know that if you want to grow $1,000 to $2,000 over a period of time, what is required is 100% growth. But what often tends to confound those who have never had the opportunity to become acquainted with the true hidden power of compound interest is the accelerating effect caused by interest that's earned in one period becoming part of the new capital base in the following period.

Let me give you two examples of how the Rule of 72 may be used.

First, in mentally calculating how long it takes to double the value of a portfolio. Second, in figuring out how long it takes inflation to halve the purchasing power of money.

IN DOUBLING THE VALUE OF A PORTFOLIO

If you have a well-diversified savings and investment portfolio that gives you a steady 6% growth rate each year, then on the surface, it would appear that to double the value of your portfolio, which means generating a total simple return over time of 100%, you would require 100 divided by 6 years, or about 17 years to do so. But actually it takes less time because of the growth boost provided by compound interest, which impressed Albert Einstein so much he declared it the 8th Wonder of the World! The snowballing growth of a compounding portfolio means you can reach this target faster than is generally expected based on mere linear mathematics (such as straight addition).

Before I show you how the Rule of 72 might be used to quickly generate the correct answer to a compound interest calculation, let's do things the long, slow way...

If you begin with $1,000, after one year you will have $1,060. If we then multiply 1.06 to that new base sum of $1,060, we see that after two years you'll have $1,124.

As we continue with this sequence all the way to the point at which an approximate doubling of value from the original $1,000 to $2,000 has been reached, you are welcome to follow along with your calculator to double check my numbers. To keep the presentation clearer, I'll take the liberty of rounding off the decimal places to the nearest integer:

After three years, you'll have $1,191. Let me now show you the amounts after four, five, six and so on up to twelve years: $1,262, $1,338, $1,419, $1,504, $1,594, $1,689, $1,791, $1,898 and $2,012.

Doing things through arduous calculation shows us that it takes us about 12 years to double the value of our initial investment from $1,000 to $2,000, if we enjoy a steady 6% annual growth rate. Note that if we take this seemingly magical number of 72 and divide it by the raw number representing the interest rate, in this case 6, that 72 divided by 6 = 12!

What's astounding is that this isn't a rare coincidence. Regardless of what normal interest rate we might use, say in the range of 1% through to 20%, division of the number 72 by the raw interest rate gives us a good indication of how many years it takes to double value. So, for instance, if you have a savings account that grows your money at 2% year, you may use the Rule of 72 to quickly figure out that 72 divided by 2 = 36 years is required to double your money, while an investment portfolio growing at a compounded annualised growth rate of 7.2% would double in value over 10 years.

IN HALVING THE PURCHASING POWER OF MONEY THROUGH INFLATION

Pretty much the same thing applies if we want to get a handle on how long it would take for a particular inflation rate to halve the value of your money's purchasing power. For instance, if we have a steady inflation rate of 4%, what this means is that if something you wish to buy is $1,000 today, it will cost $1,040 next year. I won't bore you with the complete sequence of compounding costs, but if you take the time to run the numbers yourself, you'll find that after 18 years, the cost of that particular item would be $2,026, which is pretty close to $2,000.

A 4% inflation rate will double the cost of items in 18 years.

Once again, we find that if we whip out that magic number 72 and divide it by the raw inflation rate, this time 4, we end up with 72 divided by 4 = 18! I think that's really cool.

Another way of looking at inflation is to consider how quickly the purchasing power of money erodes. If by the Rule of 72, it takes 18 years for a 4% annual inflation rate to double the cost of goods and services, then it is just as accurate to say that by the Rule of 72, it takes 18 years for a 4% inflation rate to HALVE the purchasing power of your cash.

If you're mathematically inclined, you will have quickly grasped the structure and importance of the Rule of 72. But if you aren't keen on numbers, I've probably given you a headache by now. So, either way, I'll stop soon.

In closing, do understand that the key reason to invest wisely for higher long-term returns than you're likely to gain from pure savings instruments like bank deposits is to keep pace with inflation or, better yet, race ahead of it. If you would like to learn more about the importance of investing, you may read my article entitled What is Investing? And if you are based in Malaysia, and reckon you might want my help in the realm of financial planning and retirement planning, you may learn more about me here.

© Rajen Devadason