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APPENDIX TO CHAPTER XIV 397 
se, it is the capital-value of such an income stream which 
1 ll vary from time to time. As has been seen, the capital- 
+ lue of such an income stream is found by dividing the rate of 
1 ome a by the average of the individual rates of interest, such 
t lin the above example, 109, 5%, 6 9,, etc., ad inf., the aver- 
+ 1 being obtained by the formula given in Appendix to Chap. 
TL §5 If such average rate of interest be called j,, the 
  
ital-value will be 2. Suppose, for instance, that the person 
J1 
a uniform perpetual income of $5 per annum. If the rate 
1 aterest to-day, ji, is 5%, the capital-value to-day will be $100. 
1 lext year, j, (the average of the future rates in individual 
1 Is, beginning at that time) is 4.99%, the capital-value will 
+3102. If, two years from date, j, be 5.19%, the capital-value 
+ sink to $98. Adopting such an income stream as a stand- 
the propositions as to impairment or increase will still be 
f | provided such impairment or increase is measured with 
lence to the variable capital-value just shown. Thus, if at 
1 nd of the first year more income than $5 is received, the 
+oial-value will be impaired by the difference, this impair- 
1 | to be reckoned with respect, not to $100, but to $102, 
t h would be the value had the income remained standard. 
® ls, the effect of a difference between real and stand- 
+ hcome may be stated in the same terms, whichever of the 
zt lefinitions of standard income is adopted. In the one case 
andard is with reference to constant capital and variable 
le; in the other, to variable capital and constant income. 
actical life, the former standard is usually employed, 
igh for certain purposes the latter would be more suitable. 
1 know of cases of investors who, twenty years ago, in- 
. at a high rate of interest, and who have taken pains 
7 to maintain the value of their capital unimpaired, 
“gh they were well aware that the rate of interest was 
ntly sinking. In consequence, these persons are now 
. when reinvesting, to suffer a large decrease in income, 
could have been avoided had they kept in view the main- 
2, not of their capital, but of their income, and laid aside 
1 %ar a certain sum in order to offset the fall in the rate of 
i*6. The reason such a procedure is not common is 
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