CHAPTER XIII

VALUE OF CAPITAL

§1

Having found what constitutes a rate of interest, we are
now enabled to pursue our study of the relation between
capital and income. We found in Chapter XI that these relations
 are of four kinds, according to whether the income
and the capital are measured in quantity or in value. The
fourth of these, ““value-return,” brought us to the concept
of a rate of interest.
The rate of interest acts as a link between income-value
and capital-value, and by means of this link it is possible
to derive from any given income-value its capital-value, 1.e.
to “capitalize’’ income.
To do this, we assume that the expected income is foreknown
 with certainty, and that the rate of interest (in the
sense of an annual premium) is foreknown, and also that it
is constant during successive years. With these provisos
it is very simple to derive the capital-value of the income to
be yielded by any article of wealth or item of property; in
other words, to derive the value of that wealth or property.
 That value is simply the present worth of the future
income from the specified capital. This is true whether
the income accrues continuously or discontinuously;
whether it is uniform or fluctuating; whether the installments
 of income are few or infinite in number.
We begin by considering the simplest case, that, namely,
in which the future income consists of a single item accruing
 at a definite instant of time. If, for instance, one holds
a property right by virtue of which he will receive, at the end
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