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 rela- 
tions 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 fore- 
known 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 prop- 
erty. 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 install- 
ments 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 accru- 
ing at a definite instant of time. If, for instance, one holds 
a property right by virtue of which he will receive, at the end 
202