200 NATURE OF CAPITAL AND INCOME [Cmar. XII 
terms of a perpetual annuity, or the premium on the price 
of this year’s goods in terms of next year’s goods. These 
two definitions of the rate of interest we have found to be 
interchangeable when either one of them is assumed to be 
invariable; but when this condition is not fulfilled the two 
are not interchangeable. 
Secondly, not only does the rate of interest have the two 
distinct meanings which have been given, but each mean- 
ing is subject to various interpretations, according as the 
interest is payable or reckoned annually, semi-annually, 
quarterly, etc., or continuously. 
Thirdly, as alternatives to the rate of interest we may em- 
ploy the rate of discount and the rate of capitalization. 
Both of these magnitudes also apply either in the price sense 
or the premium sense. Furthermore, like the rate of in- 
terest, they apply somewhat differently according as the 
reckoning is annual, semi-annual, quarterly, ete., or con- 
tinuous. 
The following table illustrates the various magnitudes 
which have been considered :* — 
EQUIVALENT RATES OF INTEREST, D1scoUNT, AND CAPITALIZATION 
  
  
  
  
  
A B C D 
Reciprocal 
Rate of Rate of of 4, or Recipro- 
Interest | Discount Rate of cal of B 
Capitalization 
Reckoned annually . . | 4.00% 3.85% | 25.0 yrs. | 26.0 yrs. 
Reckoned semi-annually | 3.96% | 3.88 % 25.3 yrs. | 25.8 yrs. 
Reckoned quarterly . . | 3.94% 390% | 25.4yrs. | 25.6 yrs. 
Reckoned continuously 3.929 | 3.92% | 25.6 yrs. | 25.6 yrs. 
  
  
  
  
  
  
Since the sixteen magnitudes in this table may be taken 
either in the price or the premium sense, and since, when in- 
1 For their mathematical * dimensions,” see Appendix to Chap. 
XII, § 8.