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 con- 
tinually 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 depre- 
ciation 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 deprecia- 
tion 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 rein- 
vested 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