392 NATURE OF CAPITAL AND INCOME

represented in Figure 48 by AB, CD, EF, and GH (read in the
order of futurity), the remotest item, AB, is discounted by
means of the discount curve BC, and the next to the last item
is added to the capital-value at C, bringing the capital-value to
the point D, from which the next discount curve DE is drawn,
and so on until we reach the point I IJ is thus the capitalvalue
 of the given series of income items.
In this way it is possible to review all the special cases
of capitalizing income which were considered in Chapter XIII,

 

 

 

F1a. 48.

and correct them for the general case of a rate of interest
which is variable but foreknown. Such a calculation, however,
 is of very little practical consequence, inasmuch as the
variations in the rate of interest are seldom if ever foreknown.
Were it worth while to pursue the subject, it would
be convenient to simplify the calculations by substituting,
where possible, for the series of rates of interest #, iy
i, etc., an average, j, such that if the given series of income
 items were discounted uniformly according to the rate
of interest j, we should obtain exactly the same present
value as when the several separate rates 4, 1a, is etc. are
employed. The formula for the average rate of interest j of