224 NATURE OF CAPITAL AND INCOME [CHar. XIIT

as the future income approaches, and falling suddenly as the
installments are successively passed by and acting in a
contrary manner before and after an outgo. This oscillation
 of capital-value ends finally at zero, when the
life or service of the article or group is ended. It also often
begins at zero, when the instrument or group is one that is
newly acquired or produced. These changes constitute,
as it were, a sort of life history of capital-value.!
Tt may seem to some readers that there is an exception
to the rule that the value of capital is the discounted
value of its expected income, in the case where the
income which might be received from the capital is Indefinitely
 postponed. This is the case in which the ‘principal”
 accumulates ab compound interest so that no “ interest”
 is withdrawn. If a person has a deposit of $1000
in a savings bank and leaves it there to accumulate at 4
per cent until it amounts to double that sum, which will
happen in about eighteen years, the $1000 does not appear
to him to be the discounted value of any income. If he
thinks of it as the discounted value of anything at all, it
will be of the $2000 of capital which he expects to own at
the end of eighteen years. It is perfectly true that the
capital-value of $1000 is the discounted value of the future
capital-value of $2000; but the latter capital-value is
itself the discounted value either of some subsequent
income, or, in turn, of a capital still further deferred, and
so on indefinitely. Actual income is hoped for sometime,
 even if it be not for a million years. The present
$1000 is the discounted value of that ultimate income, however
 far distant. A perpetual accumulation is, humanly
speaking, out of the question. But if such perpetual
accumulation be regarded for the moment as possible, it
may still be interpreted as a perpetual postponement of
possible income; so that even in this case the $1000 may

1 For mention of the case where the rate of interest changes and its
changes are foreknown, see Appendix to Chap. XIII, § 15.