192 NATURE OF CAPITAL AND INCOME  [Cmar. XII

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his capital, whereas in England he can get but $30,000, and
will, therefore, be just half as wealthy in actual income.

§2
The rate of interest has many meanings, and since the
concept is so vital to our study, we shall specify carefully,
in the present chapter, what these various meanings are.
The meaning implied in the previous section postulates the
existence of a perpetual annuity, v.e. a uniform and perpetual
 flow of income. Although such an annuity does
not actually exist, it is often convenient to employ it as
a vehicle of thought. Suppose $10,000 to-day will secure
a perpetual annuity of $400 per year payable annually,
the first payment accruing one year from the day of purchase;
 then the rate of interest is said to be four per cent
per annum payable annually; that is, the rate of interest
(when the interest is payable annually) is the ratio between
the rate of flow of a perpetual annuity and its equivalent in
present capital.
In case the income accrues semi-annually the case is
slightly different. Let $10,000 to-day yield a perpetual annuity
 of $400 a year in semi-annual payments of $200 each,
the first payment being due six months from date. Then
the rate of interest is said to be four per cent per annum
payable semi-annually.
That these four-per-cent rates are not equivalent to
each other is well recognized in practice, and can be made
evident in various ways. The holder of the semi-annual
annuity has a slight advantage over the holder of the annual
annuity, because he receives half of each year’s income
six months earlier. He may, in fact, convert his income
of $200 twice a year into an income of $404 once a year;
for in six months, besides receiving his first installment of
$200, he may receive $10,000, by selling his annuity. He
may then reinvest the entire $10,200 on the original terms,
4 per cent payable semi-annually, and hence obtain a per-