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