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 indi- 
cates 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,