Recently I received from my bank a letter that emphasized the value of opening a savings account. "If you put $50 a week into a bank savings account, starting at age twenty, by the time that you are sixty you will have a retirement nest-egg of more than three-quarters of a million dollars - close to seven and a half times what you put in."

I was tempted to write back, pointing out that for me, starting at age twenty would require the aid of a time machine. I also felt like saying that implicit in their arithmetic was an assumed steady interest rate on the money of eight percent per year. If they could guarantee me that, today, I would consider opening an account with them at once.

The main point that the bank was trying to make is a valid one, namely that compound interest - interest accumulating on interest - is a powerful mechanism for growth. This is true in many fields other than finance. Let us look at the idea of compound interest as we encounter it in everyday life.

As one spectacular example, consider yourself. You went from being a single fertilized egg in your mother's womb to being a full-grown baby in ten months (I know it's a little less time than that, but I want to keep the arithmetic simple). A human being contains about a thousand trillion separate cells. An embryo does not develop from a cell to a baby at a constant rate of growth, any more than the interest rates offered by your bank remain constant. The fractional growth is much slower in the final months than the early months. Suppose, however, that you had developed at a constant rate until you were delivered to your proud parents. What would your personal "interest rate" be, the rate at which you grew in size?

The answer is a substantial twelve percent per day. Each day, your growing body had on average twelve percent more cells than it had the day before. This sounds, and is, impressive, but it is nothing when compared to the performance of many bacteria. In an appropriate environment of nutrients, bacteria can replicate themselves every twenty minutes. If we wish to translate this to an interest rate, it no longer makes sense to think of annual, or even of daily, rates of compounding. The interest rate for a thriving colony of bacteria is 3.5 percent per minute. If no other process were involved, a single bacterium would become several billion trillion bacteria in a single day.

Of course, some other process must be involved, since the worldwide population of bacteria remains roughly constant. Bacteria are being destroyed (usually eaten) as fast as they are produced. This balance holds for almost all living organisms, with a couple of exceptions that I will come to shortly.

We can find an equivalent to being eaten, within the world of finance. The agent that gnaws away at your savings account is invisible, and no banker urging you to save will ever mention it. It is, of course, inflation. Anyone in business who wants to know the real value of a long-term contract must calculate its worth in present-day dollars. This in turn requires an assumption as to future interest rates, which no one, not even the Federal Reserve Board, is able to predict. So everyone guesses (and calls it an estimate).

High inflation, as many people learned during the late 1970s, can have a disastrous effect on the buying power of savings. To return to the example with which I began, should the rate of inflation over the next forty years exceed eight percent, at age sixty there will be less money in the bank, in terms of buying power, than my twenty-year-old invested.

I mentioned that there are exceptions to the apparently universal law in which organisms multiply and are killed off at equal rates. One we have already considered. A developing human spends the first months of life in the womb, where it is protected from outside attack and can grow unimpeded.

A second example where growth rate exceeds dying rate is in the area of human population. In 1800, the number of people in the world was about one billion. Two billion was reached about 1930; three billion in 1960; four billion in 1975; five billion in 1988, and we are now at about six billion. The "interest rate" on the growth in the number of people for the past two hundred years has not been fixed. Defining a generation as twenty years, we have for 1800-1930, 11.2 percent growth per generation; for 1930 to 1960, 31 percent; for 1960 to 1975, 47 percent; for 1975-1988, 41 percent; and for 1988-2001, 32 percent.

That whopping growth rate from 1930 to the present day was caused not by increased birth rates, but by a startling decline in death rates, particularly infant mortality rates, in many parts of the world. That led, as recently as fifteen years ago, to alarming predictions. By the year 2050, the world would be staggering under the load of twelve or thirteen billion mouths to feed. That estimate is changing. Countries including China, Brazil, and a number of European nations are moving to a situation in which the birth rate is or will soon be less than the death rate. In banking terms, this is equivalent to a savings account with a negative rate of interest. Italy, for instance, with a birth rate approaching 1.8 children per family, has a negative growth rate of ten percent per generation. Population analysts, extending this trend into the future, predict a population in 2050 of eight or nine billion people, followed late in the century by an actual decline in world population. A change of this kind, from population growth (positive interest rate) to population decline (negative interest rate) will have other major effects on the world. I will address these in another column.

Meanwhile, let me invite you to examine the interest rate being charged on your credit cards, and compare it with the interest rate paid by your bank on your savings. The difference between these two is often startlingly large. It demonstrates another kind of life/death cycle. Very high credit card interest rates produce more bankruptcies, which produce more bank bad debts, which are compensated for by even higher interest rates on the remaining credit card holders.

Are you in the latter group? Then you have every right to feel irritated. Complain. Or do what I do, pay off the credit card balance every month, and have a few weeks' free use of the bank's money.

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