Impact of Percentage Difference in Investment Difference

What is the difference between 3 per cent and 6 per cent annual income on an investment of $1,000? For just one year, the answer 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.

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.

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 rein¬vesting 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 per cent income per year.

   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.

GROWTH  OF  $1,000 CAPITAL  WITH INCOME REINVESTED SEMI-ANNUALLY

Number          At an Annual Rate of Increase of
of Years                 3%                  6%                  9%
      0             $1,000          $ 1,000          $ 1,000
      5                1,160               1,340               1,550
     10               1,350               1,810              2,410
     15                1,560              2,430             3,750
     20               1,810               3,260             5,820
     25               2,110               4,380              9,030
     30               2,440              5,890           14,000
     35               2,840              7,920           21,800
     40               3,290            10,600          33,800
     45                3,820            14,300          52,500
     50                4,430            19,200          81,600

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