APPENDIX TO CHAPTER XIII 385 
such installments, or the annual rate of income. Therefore 
OK, being of the same length, also represents this annual rate 
of income. 
In other words, the direction from O to ¢ lies along a paral- 
lelogram of which the side OK represents the annual rate 
of income and the side OH' a chord of the discount curve 
OP. 
Now it is evident that if, instead of a semi-annual installment, 
we assume greater frequency, the same statement will apply 
except that the point will be nearer 0. By proceeding in this 
  
  
  
  
  
  
  
  
Fic. 44. 
manner the chord OhH' approaches the tangent OH as its 
limit, and the parallelogram OH'Q'K becomes at the limit 
the parallelogram OHQK as originally described. That is, its 
sides are OK, the annual rate of income, and OH, the tangent 
to the discount curve drawn from O to a vertical line one year 
to the left. 
That this construction and its demonstration bear a striking 
analogy to the construction and demonstration which apply to 
2¢