What is the difference between 3 per cent and 6 per cent annual income on an investment of $1,000? For just one year, to calculate interest is easy: it's $30. And as long as the in­come is spent each year, while the principal amount re­mains unchanged, the answer is the same, year after year.

But a man who is saving from salary naturally reinvests his income from investments, probably automatically. With this simple step he begins to receive compound interest, and the long-term effects of this compounding of income can be weird. Starting with $1,000 capital, at 3 per cent the income the first year is $30. With this income added, the amount invested for the second year is $1,030, and 3 per cent of this is $30.90 income. Repeating this process in the third year, principal is $1,060.90 and income is $31.83; and so on. As you can see, there is increasing value to calculate interest this way.

Now look at the effect of reinvesting income when the annual rate is 6 per cent. Starting again with $1,000, in­come the first year is $60. The second year the principal is $1,060 and income is $63.60. The third year the principal is $1,123.60; income is $67.42; and so on. '" It is only in the first year, before reinvesting starts, that the difference between 3 per cent and 6 per cent is just $30, and only in that year is 6 per cent income merely twice as large as 3 per cent. In the twenty-fifth year of reinvesting at 3 per cent, principal and income are twice as large as at the start; but at 6 per cent they are four times as large as at the beginning, so that 6 per cent income in that year is not two but four times 3 per cent. This can be incredible when you calculate interest with larger sums of money.

Rather than deal with higher sums, let us consider a still longer period of years. Suppose that on a boy's twentieth birthday his father celebrates the occasion by announcing: "Son, I am making you a present of $1,000, but not in cash. For fifty years you must keep it invested, and whenever you receive income from it, you must add that income to the principal. Fifty years from now you will be seventy years old, and then you can use the accumulated fund as you please."

How big will the fund be? The first of the two following tables gives a few of the possible answers. The 3 per cent column in that table indicates the sort of results obtainable with bonds and savings deposits. After fifty years of rein­vesting at 3 per cent a year compounded semi-annually, the fund will be well over four times the original amount – a far better result than could be obtained from merely hoarding greenbacks. Even among people who consider themselves careful investors, many are not receiving as much as 3 percent income per year when they calculate interest.

The 6 per cent column of the two tables is intended as an approximation of long-term average results with a well-managed, diversified assortment of common stocks in a period without any change in business prosperity—assuming such a period is possible. Probably this 6 per cent will not be all income, strictly speaking. On common stock only part of the return is apt to be in dividends, the other part taking the form of growth in value per share. As long as all dividends are reinvested, the thing that matters is the combined effect of dividends and growth in share value, and that is what the 6 per cent is intended to represent. In fifty years at 6 per cent, the fund will be nineteen times the original amount, and over four times the amount accumu­lated at 3 per cent when you calculate interest this way.

GROWTH OF CAPITAL BY INVESTING $10 A MONTH FROM SALARY AND REINVESTING SEMI-ANNUALLY ALL INCOME FROM CAPITAL

The 9 per cent column of the tables is offered as a rough indication of results with the same sort of common stocks as in the 6 per cent column, but during fifty years in which business prosperity has increased as it has done in the twentieth century up to 1959. The 9 per cent includes the combined effect of reinvesting dividends semi-annually, and growth in value per share of stock. After fifty years of 9 per cent increase, the fund will be eighteen times as large as at 3 per cent.

Suppose another boy, lacking a parental gift of a nest egg, launches his own program of saving by small in­stallments. Starting on his twentieth birthday, he saves $10 a month out of his salary. Twice a year he invests his new savings, plus all income received from previous in­vestments. By keeping this up for fifty years, how big a fund will he accumulate once you calculate interest?

Some of the possible answers are given in the second table. By merely hoarding his savings, at the end of fifty years he has just the $6,000 he held out of his salary. With investments yielding 3 per cent a year, he more than doubles his capital. But with an annual increase of 6 per cent on the long-term average, he accumulates almost three times as much capital as at three per cent. And if the annual increase is 9 per cent after fifty years his capital is almost eight times as large as at 3 per cent.

Of course, nobody can expect to save exactly the same amount of money every month for many years, or always to receive the same rate of income or growth in value. Our examples are oversimplified in order to bring out the difference   between   rates   of   increase.   The   tables   show that in as little as five or ten years of reinvesting, the rate of increase makes a pronounced difference in the amount of capital accumulated.

Suppose that two men are both sixty-five years of age and are about to retire. Smith has been saving $20 monthly from his salary, starting twenty years ago when he was forty-five. Jones has been saving $10 a month, half as much as Smith, but he started when he was twenty-five, so that he has been saving for forty years—twice as long as Smith. Each man has saved a total of $4,800 from salary, and both men have placed their savings in the same sort of investments, increasing 6 per cent a year. Have they ac­cumulated the same amount of capital?

Smith has double the amount shown in the lower table in the 6 per cent column on the twenty-year line, or $9,040. But Jones has the amount in the same column on the forty-year line, $19,300. The length of time that a reinvesting pro­gram is continued can be considerably more important than the total amount saved from salary. The early bird catches more worms when you calculate interest.

Now let us look at two other men who have both been saving and reinvesting for the same thirty years. Brown has been taking $20 monthly from his salary, and on his investments his annual yield has been 3 per cent. Black has been saving only $10 a month from salary, but his in­vestments have increased 9 per cent a year. Which man has accumulated more capital?

Brown has twice the amount in the lower table on the thirty-year line in the 3 per cent column, or $11,540. But Black has the amount on the same line in the 9 per cent column, or $17,400. Although Black saved only half as much as Brown from salary, still he has accumulated con­siderably more capital. In long-term reinvesting, the rate of increase on capital invested can be more important than the amount saved from salary.

To show the full effect of a difference in the rate of in­crease, we need to include what happens after a man has retired from earning an income and, instead of further reinvesting, is spending his income from capital. Continuing the last example, suppose that after thirty years of saving, Brown and Black both begin to spend their income. On Brown's $11,540 capital, he receives 3 per cent income, or $346 a year. Black's income, including growth in value of stock, is 9 per cent of $17,400, or $1,566. Black's retirement income is more than four times as large as Brown's, al­though he saved only half as much from salary as Brown did.

That a difference in the average annual rate of return, or in the length of time an investment is held, when you calculate interest can develop such a contrast in long-term results as shown above is a ma­jor factor in causing investing to be such a queer business. And it is equally strange that most investors pay so little attention to the effect of selecting a type of investment that is likely to have a high average rate of return.