Compound Interest Is a Many-Splendored Thing

But Investors Need Caution in Applying It to Corporate Equities

Aug 6, 2009 Howard Bryan Bonham

In much of the advertising by financial institutions today, the practice of paying compound interest on customer deposits or assets is described as "magical."

Does a poetic investor, if there is such a conflicted soul, visualize a Walt Disney princess with a wand, sprinkling gold dust from high above frantic traders on the floor of the New York Stock Exchange?

The Internet portal, "Financial Web," takes a more utilitarian approach to compounding interest, heaping the following lavish praise on the practice: “It’s no wonder that Albert Einstein called compound interest ‘the eighth wonder of the world.’”

What Happens When Interest Income Is Compounded

Magical or wondrous is a bit fanciful for what really happens. Compounding interest is simply the process used by a financial institution- a bank for instance- of adding new interest periodically to the depositor’s original amount and adding in the accumulated interest, from prior compounding periods.

The effect is to pay interest on interest, causing the original principal to grow exponentially. Rather than magic, compounding is simply a process of causing money to replicate itself, although not quite as rapidly as a hutch of randy rabbits might accomplish. Every savings and loan depositor knows how agonizingly- slow passbook deposits grow.

Interest Rate Is the Price of Renting Money

The key variable – interest rate – is the price of renting money. It is expressed as a percentage of the principal amount, set by individuals or enterprises that have accumulated a store of loanable funds. Basically, there are two ways to calculate how interest is paid, for the use of an investor’s money: First, in the case of simple interest, only the interest income on the original amount is added, in each interest payment period.

As explained above, when compound interest is paid, interest on the original amount and the accumulated interest from each prior period are added. Rival institutions offer plans with a variety of compounding periods.

The exhibits below show the formulas for the popular versions, although there are even more variations. In spite of the advertising ballyhoo extolling the frequency of compounding periods offered by institutions, in the end result there is not a great deal of difference in results.

Caution Urged in Applying Compounding to Stock Earnings

On Wall Street, where new products and concepts often create as much business volume as booming corporate performances, stockbrokers and analysts tend to apply the compounding “magic” to corporate earnings. For them this euphemism provides two selling points:

It can subtly raise equities to the safer risk zone of higher grade securities, like preferred stocks or debentures.
It can make a stock’s compound earnings rate seem, by comparison to lower risk securities, quite spectacular.

The application of the compounding concept to common stock earnings is partly salesmanship and partly a reasonable facsimile of what can happen in an earnings progression, during a company’s normal operations. However, it is important that the investor realize that when a stockbroker or analyst says a company’s earnings are compounding at a certain rate, it’s a rough approximation of a very precise mathematical process

Continuous Compounding Could Make Sense for Multinationals

In keeping with that precision, the formulas below calculate how much a present value will grow, when earning either simple or compound interest. The math can get fairly complex, if there is more than one compounding period a year, or if the payer applies continuous compounding.

Although not used generally, the variation known as continuous compounding better describes many corporations’ earnings. For instance, multinationals operate around the clock – 24/7.

"Rule of 70 or 72" Is Shortcut for Estimating Compounding Rate

For the mathematically challenged (and who is not?), there is a shortcut to figuring a compounding rate; however, its path is primitive and rutty. While not as precise, the shortcut does enable investors to come reasonably close to estimating a compounding rate, in many cases. The shortcut is called the “Rule of 70 or 72.”

It works like this. By dividing the number of years required for a company’s earnings to double into either “70” or "72," whichever dividend produces a whole number. The quotient can be used as an approximation of the company’s compound growth rate, over that number of years. On its Website, the New York Federal Reserve Bank uses this method to estimate how soon interest income compounding at a certain rate will double.

General Electric Earnings Displayed 12% Growth Using Rule

Here is an example of using Rule of 70 or 72, for General Electric common stock. GE reported earnings per share grew from $1.52 in 1993 to $3.19 in 1999:

Divide earnings in the final year by earnings in the initial year, to see if they were close to doubling ($3.19/$1.52 = 2.1)
Accept 2.1X as a doubling
Divide 72 by six, the number of periods it took earnings to double
The quotient of 12 indicates GE’s earnings grew at a compounded rate of 12%.

Doing the math on an electronic calculator produces a 13.2% compounding rate, compounded annually, for GE’s earnings during that period. Not precise, but the shortcut is a reasonable approximation of reality.

Rule of 70 or 72 Not Rocket Science, But It's Simple

In its guide for investment beginners, the SEC says reading company financial statements is not rocket science. Using the Rule of 70 or 72 is not rocket science either; but it is simple, and can be revealing to an investor screening for high-growth stocks and willing to do additional research, on the nature of the income streams that look promising.

*The writer is a Chartered Financial Analyst (CFA).

The copyright of the article Compound Interest Is a Many-Splendored Thing in Investment is owned by Howard Bryan Bonham. Permission to republish Compound Interest Is a Many-Splendored Thing in print or online must be granted by the author in writing.