Sec. 8] VALUE OF CAPITAL 207

cessive vertical lines, four units in height, each representing
$4, and situated one unit of time apart.’
If the annuity is “deferred,” i.e. does not begin till some 1]
future time, its present value is the discounted value of

—
slg [3

 

 

 

$4. 14. HM

Fia. 2.

 

that value it will possess when it does begin. Thus, interest
 being four per cent, while $100 is the value of a $4
annuity beginning to-day (by which, as we have seen, is
meant that its first installment falls due one year from
to-day), the present value of an annuity deferred one year
later will be only 1 or $96.15, and the present value of an
annuity deferred five years is 2, or $92.46. The value
of the annuity at any time before its inception at the point
A is shown by the height at any point of the discount
curve through A.
In the preceding
posed to accrue in installm
successive vertical lines.
posed to flow continuously,
sent it by an area. In the “area

e effect of reckoning interest for dif-X111,54


discussion, the income, which is supents,
 is represented by separate
But when the income is supit
 becomes necessary to repre-»”
 method, time is still

1 For further discussion of the
ferent time-intervals, see Appendix to Chap.