242 NATURE OF CAPITAL AND INCOME [Cmap. XIV

offset that depreciation by investing annually in a few
new machines, or by annually buying investment securities.
The latter type of investment is usually thought of when
the phrase “depreciation fund” is used. If the owner
of the machines follows this procedure, then instead of
the original capital being maintained at a fixed level, it is
continually decreasing, while the depreciation fund is continually
 increasing in such a manner that the value of the
two together — the machinery and the depreciation fund
— remains constant. Consequently, at the end of the
income term, when the value of the original capital, the
machinery, is entirely exhausted, the value of the depreciation
 fund in securities will have exactly taken its place.
This fact is sometimes employed in the definition of a
depreciation fund. The fund is then described as formed
of a succession of payments out of income, such that if
each be accumulated at compound interest the total will
equal the original capital at the end of the entire income
term.
The most common application of a depreciation fund is
to a bond which does not sell at par. For instance, a
$100 five per cent bond, when interest is 4 per cent, will, if
it has 20 years to run, sell at $115. The interest at 4 per
cent on this capital is $4.60, which shows that the depreciation
 fund, being the difference between the income and the
interest, is $5 minus $4.60, or 40 cents. This item of 40
cents should annually be saved out of the income and reinvested
 at 4 per cent, in order that at the end there may
still remain a capital of $115. If the last installment of
income from the bond, $105, is treated as an income like
the previous items, the depreciation fund is, in the last
year, $105 minus $4.60, or $100.40; that is, besides the 40
cents annually there should be reinvested, at the end of
the term of the bond, the $100 of so-called “principal.”
Thus we again reach the reason that the $100 of the last
payment is regarded as “principal” or “capital’’ and not