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 foreign
 exchange, to that form of property called “hills of