“Compound Interest” vs “Compound Earnings”

dividend_stocksRepeatedly I see the term “compound interest” used to describe the growth of stock market investments.  I think this is incorrect.

Strictly speaking, you only get interest from bank deposits and bonds.  If you invest any interest you earn by depositing it in the bank or buying more bonds, then you earn interest on the interest — and that’s compounding.

If you invest in stocks, you (might) earn dividends.  If those dividends are reinvested by using them to buy more stock, then you will start earning dividends on the dividends  — and that’s compounding.  But because there is no “interest” earned on stocks, I don’t think it’s right to call it “compound interest”.

Henceforth, I suggest we use “compound interest” only for investments in bank deposits and bonds … and we use “compound dividends” for investments in stocks.  We can also use “compound earnings” in a general way to refer to any investments that grow as their earnings are reinvested in the same investment.

A little further explanation:

The interest you get from bank deposits and bonds arise from a contract: you deposit your money in the bank or you buy a bond (in both cases you are, in effect, lending money and the borrower is agreeing to pay you interest), and the bank or bond issuer is legally obligated to pay you the stated interest and return your money (the principal) to you.

The dividend you get from owning stock is a portion of the profits to which you are entitled because by owning stock you become a partial owner of the company in which you purchased stock.  However, dividends are not guaranteed as there might not be any profits or what profits there are might be used for something other than dividends, such as expansion or development of new products.

Old, But Good, Advice

Browsing through an old issue of The Sabbath Recorder (A Seventh Day Baptist Weekly, published by The American Sabbath Tract Society, Plainfield, N.J., vol. 76, No. 10.), I found some financial advice from Charles Grant Miller in the form of a story. This was reprinted in the March 9, 1914 edition.

The Saving Habit

They tell a story down in Washington about the late Senator Hoar’s improvidence. A rich friend was riding to the Capitol with him on a street-car, and Mr. Hoar was expressing wonder at the ease with which some men acquire wealth.

“I have had a good income all my life,” he explained, “but never have been able to get ahead. I would like to know how money is accumulated.”

At that instant the conductor came along and Mr. Hoar handed him a nickel while the rich friend turned over a ticket.

streetcar_ticket“There is one way in which you might acquire money.” said the friend. “You could save twenty per cent by buying six tickets for a quarter, and that is a pretty good investment. The habit of saving money grows upon one, and that is a better investment still.”

This is a good deal more than a jest.

The oversight of small investments lying close at hand leads to half the world’s financial miseries.

Of course, none could get rich by investing in street-car tickets. Nor can one get rich merely through small savings in a bank. But it is generally found that the investment in street-car tickets and the savings in the bank go together, and with them go a lot of other frugal habits.

There is no more flexible law of nature than that one frugal habit begets another, and that frugal habits beget riches.

We hear of great fortunes made in a moment. But that is not the common way.

Ordinarily a great fortune is built up like a stone wall — a stone at a time.

The young man who declines to lay the first stone, because it comes so far short of a wall, will never make progress in financial masonry.

It is a sure thing that the young man who considers it not worth while to save small amounts will never have large ones to save. He is first cousin to him who declines to go to work until he can start in at a big salary.

The first savings of Mr. Rockefeller, Jay Gould and the first Vanderbilt all look pitiably small, even to the average laborer of today. But they were seed from which sprang not only increased profits but increased enthusiasm in business-building.

Small savings and investments if constantly added to and the income compounded, grow marvelously in time.

And the saving of money is a habit that grows more marvelously even than compound interest.

— Charles Grant Miller, in Watchman-Examiner.

There’s a lot of good food for thought in that story.  Let’s look at it point by point.

Income Alone Isn’t Enough

“I have had a good income all my life,” he explained, “but never have been able to get ahead….”

As long as spending is equal to income, there will never be wealth.  This is only common sense.  Or, rather, I should say, it should be common sense.  But actually, it’s amazing how uncommon this bit of wisdom is.

Imagine a water tank with water flowing into it thru a pipe at the top.  If there’s another pipe at the bottom of the tank, then the tank will never be filled: The water goes out of the tank as quickly as it goes in.  Now imagine the pipe at the bottom has a valve that can be used to reduce the amount of water going out of the tank.  If the valve is set to allow only 90% of the water to exit the tank, then the tank will fill with water.

Checking accounts work the same way.

If people spend 100% of all they earn each year, year after year, what will they have accumulated when they stop working?  Think about it.  The answer, of course, is … nothing; those people will have nothing.  (And if spending is greater than income, that’s real misery.)

Don’t be one of those people who end up with nothing.

The best way to accumulate wealth is to live on less than your income and regularly save some percentage of your income and invest it so it grows.  The Richest Man in Babylon recommends that you save at least 10% of your income.

Don’t Pass Up Good Deals

“You could save twenty per cent by buying six tickets for a quarter, and that is a pretty good investment….”

Whenever the savings you get from buying something* are greater than what you could otherwise earn if you had invested the same amount of money, then you should buy it.

In the example in the story, tickets cost 5¢ for 1 ticket, or 25¢ for 6 tickets.  If purchased one at a time, 6 tickets would cost 30¢, which is 20% more than 25¢.  There’s no investment that is certain to yield a 20% return; that was true in 1914 and it’s true today, and even moreso in the short time and with the small amount of money it takes to buy and use 6 train tickets (a rider might use 2 each day).

Apply this to your daily life.  Suppose you eat a can of beans each week — so once a month you buy 4 or 5 cans.  Now suppose the grocery store has canned beans on sale.  Say it’s buy 5 and get 1 free (like the deal on tickets in the story).  How many cans should you buy?  Your usual number, maybe 5 cans for a month of bean eating and get 1 free?  That’s okay, but not good enough.  Why not buy enough for a whole year?  Buy 50 and get 10 free!  They won’t go bad in a year.  (Check the labels.)  Remember, a penny saved is a penny earned.  Do you have any opportunity to earn a 20% return on the additional money that you’re spending on canned beans?  No.  The stock market won’t do that well, certainly not with 100% certainty, and neither will bonds nor savings accounts.  So, what are you waiting for?  Put those cans in the cart and get to the cash register!

Some years ago, a large grocery store chain closed the local store in my neighborhood.  For a couple weeks everything in the store was marked down 30%.  Then, in the final week, everything was 50% off.  My wife and I went to the store twice that last week and spent about $400 each time.  A total of $800 spent to get $1,600 worth of groceries.  It was mostly bottled, canned, and boxed goods, of course.  We were eating breakfast cereal, spaghetti, cooking oil, and canned beans from that haul for months thereafter.  But we doubled our money with those 50%-off purchases.

Every time I see a good deal on basic foods or cleaning supplies, I make it a point to stock up if I think I could use them within the next year.

* that means something that you definitely need and will use and won’t spoil or expire before you use it.

Make Saving A Habit

“The habit of saving money grows upon one, and that is a better investment still.”

Like lots of other things you should do — like eating right, exercising, being polite to stupid people — making a habit of saving money takes practice.  The more you do it, the easier it becomes.  Efficient use of money should be your goal, it should be foremost in your mind each and every time you buy something.  You can strengthen your money-saving habit by reading books and magazines, listening to radio programs and podcasts, and watching videos about personal finances.

Just as buying when you see bargains is a good financial investment, developing the savings habit is a good investment of your time and willpower.

… one frugal habit begets another, and that frugal habits beget riches.

The more you practice the efficient use of money — frugality — in one part of your personal financial affairs, the easier it will be to apply it to others.

Slow And Steady Is the Surest Way

We hear of great fortunes made in a moment. But that is not the common way.

It’s the unusual, the uncommon, that most often receives the most attention.  (As the saying goes, “1,000 planes safely land today” isn’t likely to be a newspaper headline.)   So, it’s the rare cases of people getting rich quickly that gets the most attention.  A fortune made slowly, acquired through years of working, saving, and investing is the more common occurrence, but you are unlikely to read much about it unless you make an effort.  Your best chance to acquire wealth, in fact, it’s almost a certainty, is the tried-and-true method of living below your means, spending less than your income, saving at least 10% of every dollar you earn, and investing the savings to earn long-term compound growth.

Accept the Fact That You (Probably) Have To Start Small

It is a sure thing that the young man who considers it not worth while to save small amounts will never have large ones to save.

Don’t wait until you have a large income to start saving.  Start now.  Right now.  Chances are good that your income will grow as you advance in your career.  But small amounts you save and invest now have the advantage of having more time to grow.  To grow the kind of personal fortune you’ll need to be secure after you retire, you will need to invest…

Small Amounts … … For a Long Time
Middle-size Amounts … … For a Mid-length Time
Large Amounts … … For a Short Time

Just remember, at least 10%.  That percentage of a small earnings will be a small amount, and as your earnings grow, that same percentage will be a larger amount of larger earnings.

The Most Important Thing to Remember

Small savings and investments if constantly added to and the income compounded, grow marvelously in time.

It’s all right there in one sentence

  • A small amount, just 10% of your earnings,
  • consistently put aside and invested,
  • subjected to the miracle of compounding.

That’s all you need to know.  That’s all you need to do.

The Cost of Credit Cards

Data from the Federal Reserve show that Americans owe close to 1,000 billion dollars of revolving debt* (which I’ll refer to as credit card debt).

Dividing the total credit card debt ($1,000,000,000,000) by the adult population of the United States (the 245 million (245,000,000) persons over age 18) shows us that, on average, every American adult carries a total balance of about $4,000 on his or her credit cards.

Note that this is an average for all adults.  Because we know that some adults have no credit card debt, we can be certain that the average total credit card balance of adults that do carry credit card debt must be higher than $4,000.  Many of them carry these balances for months, or years, or decades.

How much does it cost to carry a credit card balance?

The answer depends on two things:

  • the size of the balance
  • the credit card’s interest rate

Let’s assume Joe College gets his first credit card.  A short time later he has spent $1,000 — all charged on the card.  Thereafter, the credit card balance doesn’t go much higher (let’s say that’s close to the card’s credit limit, and Joe’s a smart guy; he knows he’ll be hit with an penalty fee if he goes over the limit and it will be bad for his credit score).  If Joe paid off the entire $1,000 as soon as he got the bill, then there’d be no balance and therefore no interest charge.  But that’s not what happens.  Joe makes payments in an attempt to pay it off, but too-often he gives in to temptation and uses the card to buy something he wants, or there’s something he urgently needs and he charges it.  Thus, the balance is sometimes a little below $1,000, sometimes a little above $1,000, but it averages $1,000 for an entire year.

Most credit cards have interest rates between 10% and 30% per year.  People with good credit scores (who are probably likely to have low balances) might get cards with rates that are lower, while those with bad credit scores might have cards with interest rates that are even higher. So let’s assume the interest rate on Joe’s card is 15%.

The average balance on Joe’s card is $1,000 and he pays 15% interest per year.  How much does that cost him?

The annual amount of interest paid is a simple calculation of the interest rate as a percentage of the average balance, or:

[interest rate]/100 × [$ average balance] = amount of interest paid per year

which in our case is:

15/100 × $1,000 = $150


0.15 × $1,000 = $150 **

The $150 is broken down into monthly changes of $12.50 that are added to each month’s bill. If Joe paid only $12.50 per month, the $1,000 balance would never be reduced.  If he didn’t even pay the $12.50 interest change each month, his debt, the credit card balance, would grow as the interest would be compounded.  (His debt would also grow because he’d be hit with a late fee that would almost certainly be even higher than the month’s interest charge.  A payment greater than $12.50 would reduce the balance by whatever amount was additional to the interest.

We assume that Joe makes the payments that are normally required, which takes care of each month’s interest charge and applies some additional amount to the balance — but, as already noted, Joe keeps making purchases with his credit card, so the average balance is continually at $1,000.

This costs him $150 per year.  Consider that for a moment.  After 7 years, Joe will have paid more than $1,000 in interest, effectively doubling the cost of the first $1,000 worth of purchases he made soon after he got the card.  If he keeps going he will pay for those purchases several times.  After another 7 years, the credit card issuer will have another $1,000 of Joe’s money, … and so on for as long as Joe carries that balance on his credit card.  If Joe ever pays late or misses a payment on this credit card or any other debt, it’s quite likely that the credit card issuer will increase the interest rate on Joe’s card.  If the rate goes up to 20%, Joe will pay $1,000 every 5 years.  At 30%, he will pay $1,000 in interest charges every 3 and 1/2 years.

borrower_is_slaveLet’s remember that Joe’s spending spree stopped when he reached the card’s credit limit.  After that — after he charged that initial $1,000 — he was able to keep new charges on his credit card and what he was able to pay in equilibrium.  It’s that initial $1,000 that made Joe a borrower.  If he had been able to find that equilibrium when the credit card balance was $0, and kept his average balance at zero by charging only what he could afford to pay off each month, he would have saved that $150 each year.

The Bible says that the borrower is slave to the lender.  That should make us wonder: What was it, in that first $1,000 of charges, that was so important, so essential, that Joe had to have it, even at the cost of turning himself into a slave?  There’s an excellent chance that after he’s paid over $1,000 in interest, Joe can’t even remember what he’s paying for as he finishes paying for it for the first time and begins paying for it the second (or third …) time.  As the old saying goes, the purchase should outlast the payments.  If Joe can’t even remember what it is he’s paying interest on, can it be important enough to pay for it over and over again?

Think how much better off he would be if he had resisted the temptation to over-use his credit card.  If he had cooked dinner at home instead of going out to a restaurant, if he had gotten some new (to him) clothes at Goodwill, if he had gotten some free furniture from Craigslist or hand-me-downs from friends or family.  Had he done that, he would have been at least $1,000 richer every 7 years.

Now consider that the average American has a credit card balance of over $4,000.  Take a look at Joe’s story again, but multiply every number by 4.  A balance of $4,000 at 15% costs $4,000 in interest payments every 7 years.  At 20%, it’s $4,000 every 5 years.  At 30%, $4,000 every 3 and 1/2 years (which is well over $1,000 per year!).

Look at yourself: Are you an average American?  Are you running a credit-card-interest tab (put it on the card, put it on the tab) that’s costing you hundreds, or thousands, of dollars each year?

Remember the annual-spending tip.  If you earn, say, $50,000 per year and you’re paying $500 in credit-card interest, then interest on credit-card debt is costing you a full 1% of your income.  Are you paying 1% of your income in interest when you’re not even saving and investing 10% of your income for your own future … and maybe telling yourself you can’t save 10%, there’s nothing you can cut down on.  Well, how about cutting down on the credit-card interest you pay?

The moral of the story should be clear: If you don’t have a credit card balance, do everything you can to avoid getting one.  If you have one, do everything you can to pay it off.

* Revolving debt is basically what people owe on bank-issued credit cards and retailer-issued store and gas cards, which allow the borrower to make additional charges without any additional application process. Thus, many borrowers add new debt as fast as they pay off old debt. Home equity line of credit (HELOC) loans would also seem to fall into this category, but the Federal Reserve does not include loans secured by real estate in total revolving debt.

** The actual calculation used by credit card issuers is a bit more complex.  It involves dividing the interest rate by the number of days in a year (~365) and multiplying that by the average daily balance each month.  But our approximation works well enough for our purposes.

Einstein, Algamish, and Compound Interest

“Burritt’s Universal Multipliers for Computing Interest, Simple and Compound” by Elijah Hinsdale Burritt

Albert Einstein probably never said,

  • “Compound interest … one of man’s greatest inventions.”
  • “The most powerful force in the universe is compound interest.”
  • “Compound interest … the greatest mathematical discovery of all time”
  • “Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.”

At least, despite all of the appearances of these and similar quotes attributed to the great physicist in modern personal finance literature (and all I’ve seen were published long after Einstein’s departure from this sphere), I’ve never seen any that had a proper citation.

The formula used to calculate the future value of an investment with compound interest is pretty cool.  Maybe that’s what Einstein was talking about.  But I digress.

While there’s a lot wisdom in those (probably) spurious “Einstein quotes”, and I especially like the last one, here’s another saying about compound interest that I like even more (and I don’t know who said it):

Compound interest can either work for you or against you.  You decide.

Borrow money and you’re in debt.  If things go as planned, you pay all of the interest and part of the principal in a given month.  (Of course, you should pay more than just whatever part of the principal is required by the lender.  You should pay more so you can get out of debt as quickly as possible)  But if don’t manage to pay all of the interest you owe in a given month, then that interest is added to the principal.  Let that happen and you owe more than you initially borrowed.  Then you owe interest on the interest!  That’s compound interest working against you.  Another reason to avoid debt.


Put your dollars into a good investment.  They earn more dollars.  Then put those dollars you earned into the same investment.  They will earn even more dollars along with the dollars that were invested first.  It goes on forever.  That’s what’s so powerful about it.

In The Richest Man in Babylon, Algamish says it this way:

Every gold piece thou keepeth is a slave to work for thee.

Every copper it earns is its child that also can work for thee.

If thou wouldst become wealthy, then thou must keep and save.

And every coin thou keepest must work and earn, and their children must also work and earn, that all may help to give thee the abundance thou dost crave.