Sec. 2] CONCEPT OF RATE OF INTEREST 193
petual annuity of $408, in semi-annual installments of $204.
Tn six months more, or one year from the original invest-
ment, he may realize $204 of income and $10,200 of “prin-
cipal,” or $10,404 in all. Of this he may reinvest the
original $10,000, retaining $404. From this point onward
he may repeat the same annual cycles of sales and
reinvestments, and, therefore, receive $404 net, payable
once a year. He is, consequently, better off by $4 a year,
than the holder of an annuity of $400 a year, payable
annually. In other words, a rate of interest of 4 per cent
per annum, if the income is payable semi-annually, Is
equivalent to a rate of interest of 4.04 per cent per
annum, if the income is payable annually.
The same reasoning may be applied when the income
accrues at quarterly or any other intervals.!
By subdividing the time of payment indefinitely, we may
pass from an income obtained in installments to a continu-
ous flow of income. The idea of a uniform and perpetual
stream of income is nearly realized in certain cases, as in the
West, where water rights are sometimes bought in the form
of a “miner's inch” — a perpetual flow through a square
inch opening under a head of six inches. Let us suppose
that the water is worth $100 a year. If the right to such
a perpetual and uniform flow can be bought for $2000, the
rate of interest is five per cent “reckoned continuously.”
We thus reach the conclusion that there are various
senses of the rate of interest, according to the frequency
of payment, namely, —
The rate of interest per annum, income payable annually.
The rate of interest per annum, income payable semi-annually.
The rate of interest per annum, income payable quarterly.
The rate of interest per annum, income payable at other intervals.
The rate of interest per annum, income payable continuously.
while it is the least familiar in practice, is in
The last named, :
t natural, and lends itself the most
some respects the mos
1 See Appendix to Chap. Xs.
