Sec. 7] EARNINGS AND INCOME 243

“income.” It is simply that this $100 is always supposed
to enter into the depreciation fund, that is, to be reinvested
 and not retained as income. In case the bond is
sold at par (ie. if it yields an income equal to the
market rate of interest), there is no depreciation fund except
 the “principal” itself at the end, when the last item
of realized income ($105) exceeds the earned income of
$5 by $100. This excess, being reinvested at the same
rate, 5 per cent, will secure the continuance of the same
income.
The operation of the depreciation fund presupposes that
it is possible to invest the small differences each year in such
a manner as to accumulate at compound interest at the
rate which the original capital is earning. Such is not always
 the case, especially with articles of wealth, like land,
machinery, and so forth. In case two different rates of interest
 are involved, one for computing the capital-value of

. the given income, and another for compounding the annual

savings put into the depreciation fund, the calculation of
the depreciation fund will, of course, be more complex.!

3:7

In close relation to a depreciation fund is the “sinking
fund” employed by governments as a means of meeting
large obligations — in particular of meeting the “principal ”’
of public debts. Needless obscurity has enveloped the
“sinking fund,” especially since the intricate but fallacious
theories of Price and Pitt.
The annual contribution to the depreciation fund was the
difference between the income actually experienced and
an ideal perpetual annuity of the same present value.
A sinking fund, however, is formed from the difference
between income (or more commonly outgo) actually expe-1
 The reader is referred to the Institute of Actuaries’ Text-book,
Part I, London (Layton), 1901, where this and other problems in annuities
 are fully dealt with.