Sec. 5] VALUE OF CAPITAL 209

which is supposed to be the rate,at which water will flow
through an aperture of one square inch with a “head”
of six inches. The “first’’ inches are often so sure to continue
 as to be guaranteed. Again, if we overlook the
element of risk, the hares in joint stock companies
often exemplify perpetual annuities.
Turning from capital proper y to capital wealth, we find
in land an approximate example of capital yielding a perpetual
 annuity. Land is often capitalized on the basis of a
perpetual and uniform income, in the form of erops or other
uses. It is then valued at a certain number of years’ purchase.
 These so-called “natural and indestructible powers .
of the soil,” however, which such a calculation assumes, do
not always exist, and when they do exist, do not always
yield a perpetual annuity. Mines and quarries become
exhausted, while much land yields an irregular, increasing,
or decreasing income stream.

$5

We turn now from perpetual to terminable annuities.
Suppose that a man possesses a ten-year annuity of $100 a
year. Thismeans that he hasthe right to receive ten annual
payments of $100 each, the first falling due one year from
the present moment. It is clear that such an annuity differs
from a perpetual one by lacking the infinite succession of
payments after the ten years are past. In short, the
terminable annuity is simply a perpetual annuity dated
to-day, less a perpetual annuity deferred ten years. Therefore,
 the present value of the terminable annuity is simply
the difference between the present value of the two perpetual
 annuities. Of these two perpetual annuities, the present
 value of the one which begins immediately, interest

being four per cent, is $2500, and that of the one which is

deferred ten years is gas, or $1689. Their difference is

$2500 — $1689 or 811. Now such a difference as this, i.e.
the difference between any particular sum (as $2500) and

P