Quarterly Reports: Your Own Best Interest

If you could be any financial concept in the world, which one would you be? Inflation? Hedging? Dis-intermediation? (Sorry; "rich" is an adjective, not a concept. You've got to pick a concept.) If you were smart, you'd pick compound interest. It never fails to dazzle.

Today, for example, I bought $200,000 worth of zero coupon municipal bonds. Zero coupon means they pay no interest. Municipal means I pay no taxes. (Why taxes should be a consideration at all when no interest is paid I shall explain momentarily.) All these bonds offer is the promise that on January 1, 2014, they will be redeemed at full face value: $ 1000. I bought 200 such little promises.

Now, even a fine-arts major knows that $1000 well into the next century is worth something less than $1000 in cash today. (A bird in the hand, and all that.) But how much less?

I called my broker, a man of surpassing charm and experience, who does things the old-fashioned way. "Buy me two hundred of these New Hampshire zeros of 2014," I said. I love to talk like that.

"At what price?" he asked, his quill pen at the ready.

"They're quoted two and five eighths," I told him.

"What do you mean?" he asked.

"I mean they're quoted two and five eighths," I explained.

"What do you mean?" he asked.

When a bond is quoted at par (100), that means it's selling for 100 cents on the dollar--its full $1000 face value. When it's quoted at 55, that means it is selling for 55 cents on the dollar. Eventually, it will be redeemed at full face value--$1000--but right now, if you tried to get rid of it, $550 is all you would get. And when a bond is quoted at two and five eighths, that means it is selling for two and five eighths cents on the dollar, or $26.25 a bond. Not a lot of money.

"I mean," I said, "that each bond costs twenty-six dollars and twenty-five cents."

"That can't be right," said my broker. "It must be two sixty-two fifty." The old decimal-point trick. Not $26.25--$262.50. "Hunh-unh," I explained again, "twenty-six twentyfive.

"You mean," he said, "that for every twenty-six dollars you pay now, you get a thousand dollars in thirty-one years?"

Now you've got it."

"Wait," he said. "That can't be right."

But it is. And I bought them--$200,000 worth for $5300. It is the so-called magic of compound interest. It astonished us as children (Ripley's Believe It or Not!); it astonishes us today.

I called to tell a young investment-banker friend about these bonds. He holds two Harvard degrees and earned a bonus last year of $73,000. Money is his business. I asked how much he thought it would take to build up $200,000 in after-tax money by 2014.

"You want me to figure it out for you or just guess?" he said.

"Just guess," I said.

"Three thousand a year?"

No, fifty-three hundred once."

"That can't be right," he said, reaching for his calculator. "What rate of return is that?"

"Twelve percent a year, compounded."

"It is!" he said, a moment later, marveling at the cherrycough-syrup display of his pocket calculator.

•

It was Homer who said that $1000 invested at a mere eight percent for 400 years would mount to 23 quadrillion dollars--$5,000,000 for every human on earth. (And you can't see any reason to save?) But, he said, the first 100 years are the hardest. (This was Sidney Homer, not Homer Homer--A History of Interest Rates. Outstanding.)

What invariably happens is that long before the first 100 years are up, someone with access to the cache loses patience. The money burns a hole in his pocket. Or through his nose.

Doubtless that would have been true of the Correa fortune, too, had Domingos Faustino Correa not cut everyone out of his will for 100 years. That was in 1873, in Brazil. You could have gotten very (Continued on page 160) Quarterly Reports (Continued from page 119) tired waiting, but if you can establish that you are one of that misanthrope's 4000-odd legitimate heirs, you may now have some money coming to you. Since 1873, Correa's estate has grown to an estimated 12 billion dollars.

Benjamin Franklin had much the same idea, only with higher purpose. Inventive to the end, he left £1000 each to Boston and Philadelphia. The cities were to lend the money, at interest, to worthy apprentices. Then, after a century, they were to employ part of the fortune Franklin envisioned to construct some public work, while continuing to invest the rest.

One hundred ninety-two years later, when last I checked, Boston's fund exceeded $3,000,000, even after having been drained to build Franklin Union, and was being lent at interest to medical school students. Philadelphia's fund was smaller, but it, too, had been put to good use. All this from an initial stake of £2000!

And then there was the king who held a chess tournament among the peasants--I may have this story a little wrong, but the point holds--and asked the winner what he wanted as his prize. The peasant, in apparent humility, asked only that a single kernel of wheat be placed for him on the first square of his chessboard, two kernels on the second, four on the third--and so forth. The king fell for it and had to import grain from Argentina for the next 700 years. Eighteen and a half million trillion kernels, or enough, if each kernel is a quarter inch long (which it may not be; I've never seen wheat in its pre--English-muffin form), to stretch to the sun and back 391,320 times.

That was nothing more than one kernel's compounding at 100 percent per square for 64 squares. It is vaguely akin to the situation with our national debt.

•

Just as the peasant could fool the king, so are we peasants now and again fooled. For decades, for example, one of the most basic deceptions in the sale of life insurance has been what is called the net-cost comparison.

Without sitting you down at the kitchen table and walking you through the whole thing (it being difficult to sit and walk simultaneously), suffice it to say that whole-life insurance, seemingly expensive, could be shown by the insurance professional to cost nothing. For after 20 or 30 years, your accumulated cash value and dividends could exceed all the premiums you had paid in!

The only thing this comparison ignores is the time value of money--the fact that all those premiums, had they been accruing interest on your behalf, might have been worth far more than the amount with which the life-insurance company was willing to credit you.

"Do you realize," I have been asked angrily by life-insurance salesmen, "that we have policies now that can be paid up after just eight or nine years?" They ask it as if the companies were doing an incredible, unappreciated, magnanimous thing, when, of course, the reason no additional premiums are due after the first eight or nine years is simply that the excess charged in those years is enough, when compounded at today's extraordinary interest rates, to fund the policy forever after. There is no magic here, no magnanimity, merely the workings of compound interest.

It is remarkable how many people, while they certainly know such terms as interest and return on investment, fail fully to understand them.

Say you borrowed $1000 from a friend and paid it back at the rate of $100 a month for a year. What rate of interest would that be?

A lot of bright people will answer 20 percent. After all, you borrowed $1000 and paid back $1200, so what else could it be? Forty percent?

No. More.

If you'd had use of the full $1000 for a year, then $200 would, indeed, have constituted 20 percent interest. But you had full use of it for only the first month, at the end of which you began paying it back. By the end of the tenth month, far from having use of $1000, you no longer had use of any of the money. So you were paying $200 in the last two months of the year for the right to have used an average of $550 for each of the first ten. That comes to a bit more than a 41.25 percent effective rate of interest. (Trust me.)

Because this sort of thing is complicated, there are truth-in-lending laws requiring creditors to show, in bold type, what they're really charging for money. (Well, they show nominal rates, not effective rates, but it's close enough.) Unfortunately, no similar disclosure law applies to life insurance.

Or tuna fish.

There's this national magazine, you see, which shall remain nameless, that is published by Time, Inc., and that specializes in matters of personal finance. It ran a story not long ago, "Bargainmania," about some very strange people--among them, a man who bought 25 years' worth of laundry detergent because it was on sale and a woman who spent the better part of a day and drove 25 miles to buy 18 frozen chickens at 56 cents a pound. The next day, they went on sale at her local market for 53 cents.

One of the people ridiculed in that story was a young and handsome financial writer who shall, in fairness, also remain nameless, but who had bought a case of tuna fish years earlier at his neighborhood supermarket for 59 cents a can. "Yet for all his trouble," the story scoffed (what trouble?), the annual tax-free return on his "investment" will turn out to be only "about eight percent once the tuna is all consumed nearly two years hence."

A letter to the editor, shrill but not hysterical, was dispatched to point out that the magazine had miscalculated. Even granting its assumption that the world would be seized by a tuna glut, severely depressing prices, the tax-free rate of return worked out to about 16 percent a year, compounded, not eight percent.

The point was not so much that the case of tuna fish had turned out to be a reasonable thing to buy--which, in its own entirely trivial way, it had--but that compound-interest and rate-of-return calculations were the sort of thing that a national monthly magazine specializing in personal finance should be able to perform.

In response to the letter came a note from a very high-ranking editor at the magazine, saying he wasn't sure they "should be eating crow" just yet and enclosing a "documented analysis" explaining how the eight percent figure had been arrived at (it had been arrived at wrong)--as though all this were open to opinion rather than a simple matter of lower mathematics or, simpler still, of punching the appropriate buttons on a pocket calculator. (Those who have calculators and care, see the box on this page.)

It was one thing for an error to slip into the story--these things can happen to anyone. But once the error had been flagged?

If compound-interest-rate calculations knit your brow, therefore, fret not. You're in distinguished company.

All you really need to know--or a good start, anyway--is the rule of 72. It says: To determine approximately how fast an investment will double, divide the interest rate into 72.

Seventy-two divided by three is 24; money invested at three percent, compounded, doubles in just under 24 years.

Seventy-two divided by 12 is six; money invested at 12 percent, compounded, doubles in six years. Why does this work? No one knows. It works because it's a rule.

Because money invested at 12 percent, compounded, does, indeed, double every six years, in 31 and a half years (the time remaining on my 200 New Hampshire zero-coupon bonds), each of my little $26.25 investments will double five times and then grow for another year and a half. At that point, I will be 66 (not a pretty thought); the New Hampshire State Housing Authority may or may not be solvent; and a box of Jujyfruits may cost $48.

Wherein lie the two principal risks of these, or any other, long-term bonds: insolvency (what good is a $1000 promise if it's broken?) and inflation (Jujyfruits have already moved up from a dime a box to a half dollar).

There is always the possibility that the killer bees, already laying waste to Houston, will by 2014 reach New Hampshire and render it all but uninhabitable. Or that the backing on which these bonds rest--namely, the full faith and credit of 1800 illegal aliens in a low-income housing project--will somehow be impaired.

And, as I say, there's the Jujyfruit risk: If inflation should compound as fast as my bonds, then $200,000 in 2014 will buy precisely what $5300 buys today.

But the killer bees may veer off toward Missouri, and Jujyfruits may begin to level off. Should inflation and interest rates return to "normal" levels any time soon--four percent having been a perfectly respectable return on municipal bonds throughout much of this century, and six percent having been the rate as recently as 1978--then I will, indeed, be sitting pretty watching my bonds compound tax-free at 12 percent. (There is one teentsy-weentsy catch here, to which I will return.)

Others will have locked in high yields on interest-bearing 30-year bonds, but they will not be sitting so pretty. Most long-term bonds issued today include "call" provisions. Today's municipals are typically callable after ten years. At that point, they can be paid off. You may be locked into the Reno Desalinization Project for 40 years, but the Reno Desalinization Project is locked into you for only ten. Thus, just as you may be planning to refinance your high-interest mortgage when interest rates drop, so are most states and cities hoping to refinance their high-interest debt.

Most zero-coupon bonds can't be called. What good would it do? Calling a bond ordinarily means buying it back at par or a little above. So--go ahead! Buy back my little $26.25 investments at $1000 each! That is something even the feeblest of state controllers is not likely to propose.

In the event that interest rates do fall, there is a second enormous advantage to zero-coupon bonds. Not only am I guaranteed my 12 percent until 2014--it is 12 percent, compounded. Purchasers of ordinary long-term bonds may continue to get high interest--but what will they earn in interest on that? A bond that pays 12 percent but from which the interest can be reinvested at only, say, six percent, will grow not to $1000 from $26.25 by the year 2014 but to a paltry $305.

So much for the advantages of zero-coupon bonds. Bear in mind the following:

1. As with any long-term bonds, the issuer could go broke.

2. Likewise, if interest rates rise, the value of the zero-coupon bond will fall. Eventually, it will rise to its full $1000 face value, but eventually is a long way off.

3. The Internal Revenue Service was not born yesterday. Even though zero-coupon bonds pay no interest, you are taxed as if they did. If the bond is geared to grow by 12 percent a year to maturity, then you pay tax each year as if you'd received 12 percent interest. (The exception: municipal zeros, which, like any other municipal bonds, are Federal-income-tax-free.)

Obviously, this makes taxable zero-coupon bonds a crummy investment, except for tax-sheltered funds, such as IRAs and Keogh plans. (There they are excellent. Call your broker for details.)

4. Although you can sell zero-coupon bonds, like any other long-term bond, any time you want, the market in most of these issues will be thin. Thin, inactive markets mean big spreads for the market makers.

5. The advantages of zero-coupon bonds and their handiness with respect to IRAs and Keoghs will be reflected in their price. The more popular they become, the less attractive they will be. My New Hampshire State Housing Authority zeros, purchased at $26.25, will yield 12 percent, compounded, to maturity. By January 1983, other things being equal, they should have risen to about $30 on their long 12 percent, compounded, climb to $1000. Should they have been bid up to, say, $45, instead, there would be substantially less incentive to buy them, for at that price they would be yielding only 10.52 percent to maturity.*

6. In the case of this particular New Hampshire State Housing Authority bond issue (rated AA, no less--apparently, there's more behind them than 1800 indigent aliens, after all), there is the aforementioned teentsy-weentsy little catch. Most zero-coupon bonds can't be called. As I've said, what good would it do? But these and some other zero-coupon municipals are callable at the issuer's discretion--not at their ultimate $1000 face value but in accordance with an "accretion schedule" that starts at a pittance, like your bond, and rises each year at 12 percent.

So if long-term interest rates drop dramatically, say goodbye to your New Hampshire zeros. They will be called back in by the Housing Authority. Just one more example of the First Law of Finance: If It Looks too Good to be True, You haven't Read the Prospectus.

•

I could tell you about subzero coupon bonds, where you pay them interest; but these are not yet off the drawing board (or on it, so far as I know). I could tell you about tontines, in which not only your money but the money of all your grade school classmates compounds magnificently on your behalf, should you be the last one left alive to claim it; but these have fallen out of fashion.

Available and in fashion are the aforementioned IRAs and Keogh plans. Some 14,000,000 new IRAs were established in the first 90 days of 1982 alone. IRAs provide a discipline to save (the discipline comes in the extra taxes you pay if you don't save), and they also allow money, once under the IRA umbrella, to compound free of taxes.

But is there really any reason for a guy in his 20s, say, and maybe not even in so high a tax bracket, to bother with one of these things?

Far be it from me to counsel anything so dull. I have most of my own fortune tied up in Japanese antiques (four-year-old videotape recorders). But did you know that $2000 compounded at eight percent (after taxes) grows to $43,449 in 40 years--but to $377,767 at 14 percent sheltered from taxes in an IRA? Or that putting away $2000 a year at 12 percent, beginning at the age of 35, builds to $482,665 by 65--but to $1,534,183 if you start ten years earlier?

However little $377,767 will buy in 40 years, it will buy more than $43,449. However paltry $1,534,183, it will be less paltry than $482,665.

•

Two final notes:

1. The national magazine eventually saw the light and called to apologize.

2. The IRS has been doing some thinking about compound interest, too. Taxpayers have always been liable for interest on overdue taxes; as of January 1, 1983, however, that interest is being compounded. Daily.

"It is remarkable how many people who certainly know basic financial terms fail fully to understand them."

Time, Inc.'s magazine of personal finance assumed that 144 cans of tuna fish had been purchased at 59 cents each (the "investment") and that they were consumed ("sold") at the rate of 25 a year for 5.75 years--at 79 cents the first year, 89 cents the second, 99 cents the third, $1.09 the fourth and (because of the tuna glut) just 89 cents thereafter.

Some calculators allow you to plug in these numbers, press a button and obtain your result. Or you can look at it this way: The first 25 cans of tuna, eaten over the course of the first year, were "sold" for 79 cents each. If they had all been eaten the last day of the year, that would have been a 20-cent profit on each 59-cent purchase, or about 34 percent for the year. But because they were consumed steadily over the course of the year, one every two weeks or so, the average can in that first year's batch was held just half a year. The rate of return was, thus, twice as good--about 68 percent. On the next batch of 25 cans, bought for 59 cents and sold over the course of the second year for 89 cents, the profit per can was 30 cents, and the average holding time of the cans was a year and a half. To earn 30 cents on 59 cents in a year and a half is to earn 31.5 percent compounded annually. The third batch, held for an average of two and a half years and sold for 99 cents, represented a 23 percent compounded annual return; the fourth, 19 percent; the fifth (assuming the tuna glut), 9.5 percent. Only on the last few cans would the compounded annual rate of return have been eight percent.

Using the going rate for tuna fish--two cans were enclosed with the letter to the editor (making it a package to the editor)--the return on even those last few cans would have exceeded 17 percent.

*How do I know this so fast? I press 45 on my Texas Instruments MBA calculator and then the button marked PV (present value--what I'll paying today). Then I press 1000 and the FV button (future value--what I'll get, God willing, tomorrow). Then I press 31 and the N button (the number of years until tomorrow). Then I press CPT (compute) %1 (interest rate). I wait exactly two seconds. During this time (as I understand it), a message is bounced off a satellite and down to Texas Instruments, where a fellow in a green eye-shade with a cactus on his desk whips out paper and pencil, does the calculation and shoots it back up to New York before the Japanese even know that there has been a little bit of business to bid on. This is the same fellow who used to do the customized research reports for owners of the "Encyclopaedia Britannica" that always used to arrive a week or two after your term paper was due. He's gotten much faster.