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 os- 
cillation 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 In- 
definitely postponed. This is the case in which the ‘prin- 
cipal” accumulates ab compound interest so that no “ in- 
terest” is withdrawn.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 some- 
time, even if it be not for a million years. The present 
$1000 is the discounted value of that ultimate income, how- 
ever 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.