Albert Einstein’s Greatest Discovery: The “Rule of 72”

Compound interest is one of the most powerful financial tools that you can use toward your own and your business’s success. It is far more powerful than most people realize. It can be used for you, and it can be used against you. Fully understanding all the aspects of this powerful tool is essential for everyone in their personal and business finances. Albert Einstein has been credited for the discovery of compound interest.

“According to him this, not E=mc² was his greatest discovery, “Compound interest was not only man’s greatest invention, but it was also the most powerful force on Earth!” Those are compelling words coming from one of the most intelligent men of our time!”

(The Motley Fool).

The explanation of compound interest is a simple one. When you invest money, you earn interest on your capital. In the next year, you earn interest on your capital and the interest you earned the year before. Now this principle applies to any type of investment, debt repayment and the effects of the inflation rate on your buying power.

Compound interest is not commonly understood. Most feel that it is a lot of mathematical magic, and are unable to determine exactly how they can make their money work harder than they do. We simply determine how powerful this compound interest is by using the “Rule of 72”. By using this rule, you can fairly accurately determine how long it will take to double your money (or your debt) at a given interest rate. The rule is simple, divide the number 72 by the interest rate you are receiving (72/10=7.2), and you will find the number of years it will take to double your money. It is called the rule of 72 because at 10% interest, the money will double every 7.2 years.

You can also compute an interest rate if you are told that your money will double in “so-many” years. For example, if you needed to double your money in two years, and you would be able to figure that you would need to earn 36% interest (72/2 (years)=36%).

You can also use the rule of 72 to determine when your debt will double. An example of this would be if you borrowed $500 dollars from your friend, who is charging you 6% interest. 72 divided by 6 is 12. So, 12 is the number of years it would take for your debt to your friend to double to $1000 dollars if you did not make any payments.

You can also determine how inflation works against you. “The government tells us we have had about a 6.9% inflation over the last 15 years” (The Motley Fool). In this instance, for your buying power to stay even with inflation you must earn at least 6.9% more income each year. You can determine the time that it will take to half your buying power by using the rule of 72. At 6.9% inflation it will take just over 10 years for the buying power you have today to be cut in half.

While considering different types of investment vehicles, remember that the rule of 72 can help you make intelligent decisions including tax repercussions. “Consider this, you are earning 6% on your savings but you are in a 33% tax bracket. After the taxes on your interest, you only earn 4% interest. Using the rule of 72, it will now take 18 years for your money to double instead of 12 if it were in a tax deferred account. In this example, paying taxes on your savings can effectively cost you 6 years of growth” (Friedman).

The “rule of 72″is a rule of thumb. Like any rule of thumb, the rule is only good for approximations. It also assumes an annual percentage interest rate. It is by no means exact. At 1% interest the exact amount is 69.66 and using the rule of 72 it is 72. At 4% interest, the exact amount is 23.45; the rule of 72 is 24 years. So it is an approximation, but it is also pretty accurate, up to 20% interest.

To demonstrate the ease of using the approximate value of the rule of 72 verses determining the exact number at 10% interest, “consider the following derivation: Determine how long it takes a given principle (P) to double given either the interest rate (r) or the number of years (n). The equation looks like this:

P * (1+r/100)^n=2P

In this case solve for r=10%.

P * (1+10/100)^n=2P

Cancel the P’s :

(1+10/100)^n=2

1.1^n=2

Solve for n using logarithmic function

(Natural logarithm = ln (a^b)=b * ln(a))

n * ln(1.1)=ln(2)

n * (0.09531) = 0.693147

n = 7.2725527

Which means that at 10% interest, your money doubles in about 7.3 years” (Cilek, Chuck, 1998). The rule of 72 is a remarkably accurate and a much easier way to determine quickly how long it will take to double your money as long as the interest rate is below 20%. Above 20%, the rule becomes significantly inaccurate.

Albert Einstein truly understood the power of compound interest and the simplicity of the rule of 72. Albert Einstein called compound interest the eighth wonder of the world and mankind’s greatest invention because it is the mightiest force ever unleashed for the amassing of wealth” (Mauder). The rule of 72 is simple and powerful, yet unknown by many business owners, professionals and individuals. Remember that you can use the rule of 72 forwards and backwards. To determine the time to double an investment, or the interest rate needed to double money in a given time. If you are still wanting, you can use the rule of 113 to determine how many years it will take to triple your money.

References

Cilek, Chuck. (1998). Subject Analysis – Rule of 72. Available from http://www.ruleof72.net

Friedman, S. Morgan. Einstein: Light to the Power of 2. Available from http://www.devine-ent.com/shows/inventors/einstein.shtml

The Motley Fool (1997). Rule of 72. Available from http://www.fool.com

Mauder, Dave. The Most Powerful Force On Earth… Is It Working For You? Available from http://www.mauder.com/articles/sr_powerfullforce.htm

Reference:

• Cilek, Chuck. (1998). Subject Analysis – Rule of 72. Available from www.ruleof72.net