388 NATURE OF CAPITAL AND INCOME

the price of the stream if paid for in advance, AQ represents
 the price if paid for at the end. By similar reasoning
it may be shown that the price at any intermediate point of
the entire series is the height of any point on the one smooth
curve PQ.
This result must not be confused with that which represents
the capital-value of future income. Thus, at the point of time
0, the line O'P' represents the value of all the income items,
past as well as future, AB, AB, AB, 4B", whereas the
line O'P'" represents the value of only the future items A'BY
and A"BM.,

§ 14 (ro CH. XII, § 10)

Effect of reckoning Semi-annually, Quarterly, and Continuously, on the
Rate of Interest realized on a Stock or Store of Articles

As usual, the passage from the rate of interest reckoned
annually to the rate of interest reckoned continuously, if accurately
 considered, is not so simple as appears on the surface
and may afford to some readers no little perplexity. If we
assume, for convenience, that each article in the merchant’s
stock remains there for a definite period, called the time of
«turn-over,” and the cost of purchase and all the other costs
connected with the article occur at the time it enters the
stock, while all the receipts or gross income from that article
occur at the time that it leaves the stock, we may pass from
the case of the rate of interest «reckoned annually” to that
of the rate of interest «reckoned continuously ” as follows: —
As a first step we assume that all of the stock is bought at
the beginning of a calendar year and sold at the end, so that
the time of turn-over is one year. If the cost of the stock is
represented by ¢, including not only the purchase price but all
other elements of cost, this must represent the discounted
value of the receipts at the end of the year, which are therefore
 ¢(1+14). The net income for the year is, therefore,
¢(1 +41) —c, or ¢i. This bears a ratio to the total cost value

reckoned at the beginning of the year, namely ¢, of 2 equal
to the rate of interest, i. g
For the second step we consider the stock as half purchased