Sec. 4] CONCEPT OF RATE OF INTEREST 195

if a man borrows $100 to-day and agrees to pay it back with
interest at 49% in one year, we may conceive of him as
having sold a perpetual annuity of $4 a year for $100, and
at the same time as having bound himself to buy it back for
$100 at the end of one year. The combined result of these
operations amounts to an exchange of $100 this year for
$104 next year. It is possible to use such a simple exchange
between this year’s and next year’s money, as the basis of
an entirely new definition of the rate of interest, and one
which is independent of the idea of an annuity. When
$100 to-day is exchanged for $104 next year, the ratio of
exchange between the two sums is }§¢. This ratio is not,
of course, itself the rate of interest; the rate of interest is
the excess, or premium, of 1%, above unity. In other
words, the rate of interest is the premium, or “agio,” above
par of this year’s dollars in terms of next year’s dollars.
Such a concept of interest may be called the premium concept,
 whereas the concept hitherto employed, or the price of
capital in terms of an annuity, may be called the price concept
 of the rate of interest. To say that the rate of interest
in the price sense is four per cent means that the price of $100
of capital is $4 of income per annum forever. To say that
the rate of interest in the premium sense is four per cent
means that the price of $100 of one year’s goods is $104 of
the next year’s goods.
The premium concept of the rate of interest has been so
much emphasized, notably by Bohm-Bawerk, that it
seems advisable to repeat briefly, with respect to it, the distinetions
 as to annual, semi-annual, quarterly, ete., reckoning.
 Let us suppose that $100 to-day is worth $102 six
months hence. The rate of interest in the premium sense
is here 2 per cent for the six months’ interval, and is said
to be “4 per cent per annum payable or reckoned semi-annually.”
 Tt will be evident, however, that this is a little
higher rate than 4 per cent per annum reckoned annually.
Let us suppose that at the end of six months, at which time