204 NATURE OF CAPITAL AND INCOME [CHar. XIII 
stant a year hence; B”, that two years hence; B’’, three 
years hence; and B®, ¢ years hence. AB represents any 
present value, A’ B' the “amount” of this sum one year hence, 
A”B’ the “amount” two years hence, etc. Consequently, 
AB also represents the present value of A’B’ due one year 
hence, or of A”B” due two years hence, or of A®B® due 
t years hence. The curve AA® is an “ exponential curve,” 
this being the name given to a curve which ascends in geo- 
AD) 
  
  
B B! BY BW B(t) 
Fic. 1. 
metrical progression, 7.e. ascends so that the successive 
vertical lines, AB, A’B’, A”B”, and A""'B'" (ordinates), 
taken at equal intervals, increase in length at a uniform 
ratio. We shall, however, for economic purposes, christen 
this curve the “discount curve.” 
§2 
The principles which have been explained for obtaining 
the present value of a single future sum apply to many 
commercial transactions, especially to the valuation of bank 
assets, which exist largely in the form of “discount paper,” 
or short-time loans of other kinds. The principles also 
apply, though in combination with those of risk and for- 
eign exchange, to that form of property called “hills of