236 NATURE OF CAPITAL AND INCOME [Crar. XIV
$1000 a year for 20 years, discounted at 5 per cent. But
it is not true that $18,300 is the discounted value of the
earnings of the house, for the earnings are all less than
$1000, beginning at $918 a year and dwindling each year
until the fifty years have expired; and clearly the discounted
 value of fifty annual items each less than $1000
must be less than the discounted value of fifty annual items
of $1000 each.
Since, -then, earned income cannot be derived without
assuming realized income, and since capital-value has been
shown to be the present value of the latter, and not of the
former, it is clear that realized income is the more fundamental

 concept of the two.

§5
But so persistent is the accountant’s instinet to put aside
realized income in favor of earnings that we need to point
out in detail the confusions which arise, unless income and
earnings are carefully distinguished. We first observe that,
under the given conditions of foreknowledge, earnings and
interest are equal. Now if interest is at 5 per cent, a capital
 of $1000 invested in whatever form — land, houses,
horses, securities, or anything else — though it is said to
earn 5 per cent, does not necessarily receive an income each
year of $50. The $1000 means the present value, discounted
 at 5 per cent, of some expected income stream;
but that income stream may take any one of an indefinite
number of forms; such, for instance, as a perpetual annuity
 of $50 a year, as in the case of land; or a terminable
annuity of $100 a year for 14 years; or an income of $25 a
year for 10 years followed by an income of $167.50 a year
for 10 years. All of these are inter-equivalent, and when
discounted at 5 per cent, each of them represents a capital
of $1000.
Of all these possible forms of income it is usual to take the
perpetual annuity as the standard income (earnings) and to