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 parallelogram
 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¢