APPENDIX TO CHAPTER XIII 377 
The decrease in capital-value of the annuity, which has been 
represented by the approach of CE to the horizontal line DE 
above it, is better represented, however, by inverting CE to 
the position AB, in order that the capital-value may be repre- 
sented, as in our previous examples, by the distance from the 
D E 
  
       
  
  
TT 
Fic, 41. 
horizontal line AB below it. This change is accomplished 
in Figure 40. The value of the annuity taken after each 
installment of income is represented by the ordinate, as mA’, 
of the curve KB, and the value just before an installment 
is represented by the ordinate, as nd", of a point above this 
curve a distance equal to that installment. The value at inter- 
follows a discount curve, as mn, be- 
The result is that the capital-value 
g to the steps, or teeth, shown in the 
mediate points evidently 
tween these two points. 
will rise and fall accordin 
diagram. 
As the income items 
come more frequent and smaller, and disappear when the flow 
of income is continuous, as represented in Figure 41, where the 
become more numerous the teeth be- 
     
  
  
  
  
  
  
   
   
  
   
  
  
  
  
  
   
  
  
  
  
    
— SRE TRS RR