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

Number                Savings Amount Accumulated at an Annual
   of Years                                    Rate of Increase of
                                           3%                             6%                                9%
  5                $ 600         $  642                  $  688                      $ 737
10               1,200           1,380                   1,610                       1,880
15                1,800          2,250                   2,850                      3,660
20               2,400          3,260                   4,520                      6,420
25               3,000          4,420                  6,770                   10,700
30               3,600          5,770                  9,780                   17,400
35               4,200          7,340                13,800                   27,700
40               4,800           9,160                19,300                   43,800
45                5,400        11,300               26,600                   68,700
50               6,000       13,700                36,400                107,000

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 in¬stallments. 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 in¬vestments. By keeping this up for fifty years, how big a fund will he accumulate?
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 ac¬cumulated 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 pro¬gram is continued can be considerably more important than the total amount saved from salary. The early bird catches more worms.
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 in¬vestments 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 con¬siderably 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 in¬crease, 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, al¬though 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, can develop such a contrast in long-term results as shown above is a ma¬jor 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.