APPENDIX TO CHAPTER XIII 391 
year previous to the due date, or one year from the present, 
and rediscounting this 970.87 at 59, for one year, giving 
970.87 
1.05 
In general, if ¥ represents the item of income to be received, 
  
, or $924.30, as the present value. 
its value in one year will be and its present value, 
  
+ 1 
lm YS een 
+4) (1+) 
which formula is, of course, easily extensible to three or any 
number of years. 
If we represent the future value ¥ in Figure 47 by the line 
AB, its value in one year is CF, found by the 3% discount 
  
  
  
B 
C Ry 
D 
E F A 
Fic. 47. 
curve BC, and its present value is ED, found by the 59, dis- 
count curve DC. In other words, instead of having a uniform 
discount curve from B to D, we have a broken discount curve 
BCD, with a different percentage rate of rise for the two 
years considered. ; 
In this way we may obtain the present value of any series of 
income items precisely as before, with the exception that the dis- 
count curves are now somewhat irregular. Thus, if the series 
of income items at different points of time are of the magnitude