194 NATURE OF CAPITAL AND INCOME [Cmar. XII

readily to mathematical transformations. The first, on the
other hand, is the most frequently used in practical
computations.
§3
We have considered the rate of interest as the price of
capital in terms of income. If we consider reciprocally
the price of income in terms of capital, we shall have what
is called the “rate of capitalization.” It is measured in
years, namely, the number of years during which there
would flow an amount of income equal to the capital. Thus,
if $25,000 will buy a perpetual annuity of $1000 a year, the
rate of capitalization is “ twenty-five years’ purchase.” The
concept of ‘years’ purchase” is common in England as
applied to land rents. It is evidently interconvertible with
the rate of interest. A rate of interest of four per cent indicates
 a ‘years’ purchase” or rate of capitalization of
twenty-five years. A rate of interest of two per cent
indicates a rate of capitalization of fifty years. The rate of
capitalization has thus as many meanings as the rate of
interest, according as the income is payable annually,
semi-annually, quarterly, etc., or continuously.

§ 4

The concepts of interest which have been given depend
upon the concept of a perpetual annuity. But they can be
made to apply also to terminable annuities. Thus, $10,000
may yield at four per cent an income of $400 a year for
ten years, at the expiration of which time the $10,000, or
the “original loan,” is returned. In such a case the loan
may evidently be regarded as a purchase and resale of a
perpetual annuity. A perpetual annuity of $400 is, for the
price of $10,000, diverted to the lender’s benefit, and at the
end of ten years is restored to the borrower for the same
sum.

We may regard in this light even short-time loans. Thus,