APPENDIX TO CHAPTER XII 365

small correction, equal to the product of the rates of interest
and discount.
The relation between the rates of discount and interest
when semi-annually reckoned is analogous to the relation which
we found between those annually reckoned. We then have

the equations, y ale
r 2
7? 1 !
d =
Ba V 1 2’

whence (555) (1 +3 )=1

By multiplication and reduction,
rt
d'=1 5
We may apply similar reasoning to quarterly-reckoned
interest and discount rates.
1 "
. It follows that (142) (1-F)=%
or av dential
The same reasoning may obviously be applied to reckonings

n times a year. We then find,

HO fh eS

 

n
It is evident that if n, the number of parts into which the
im» am
be- 



year is divided, be sufficiently increased, the term
n

comes infinitely small, so that, at the limit, the rate of interest
and the rate of discount become equal. This rate for continuous
 reckoning, being the same as the rate of interest for continuous
 reckoning, is also called 8.
Unlike the rate of interest, the rate of discount is always
considered as associated with the exchange of present against
future goods, and not with the exchange between capital and
income, i.e. is taken, not in the “price” sense, but in the “premium”
 sense (the premium being, in this case, negative). We
may, however, to complete our scheme of concepts, construct
for ourselves a “rate of discount” in the sense of the price of
capital in income. We recur to the fact that the rate of