Sec. 8] VALUE OF CAPITAL 217 
the bond is reinvested, it may be that it is not equal to 
the original investment, nor, therefore, to the capital-value 
of the bond at any time before maturity. This equality 
would hold true-only in case the bond is always kept at 
par. When it is worth more or less than par the capital- 
value is more or less than the “principal,” and for this 
reason, if for no other, the capital-value should not be 
confounded with the ““ principal.” 
In order to determine whether or not a nominally five 
per cent bond really yields five per cent, we must refer to 
the price at which it sells, and while there is no neces- 
sity to abandon the terminology by which “principal” 
and “interest’’ are used with reference to bonds, these 
terms are undoubtedly misnomers and their existence is 
responsible for considerable confusion. For instance, 
insurance companies have recently been offering their 
policy holders an option between the receipt at the death 
of the insured of a definite insurance of $1300, or of a 
“five per cent gold bond” for $1000. The gold bond has 
seemed, to many policy holders, a tempting form of invest- 
ment because of the “high rate of interest,” — five per cent; 
but it is evident that such a bond, considered as the equiva- 
lent of $1300 in cash, is on a lower basis than five per cent. 
$8 
Hitherto we have considered only four special cases of 
capitalizing income, viz. (1) the capital-value of a single 
income item; (2) the capital-value of a perpetual annuity ; 
(3) the capital-value of an annuity terminable in a definite 
number of years; and (4) the capital-value of a bond. But 
it is clear that the items of income from any property may 
oceur in many other forms, may last for any length of time, 
and may be distributed through this time in any manner 
whatever. Let us, therefore, consider the general case in 
which any random series of income items, AB, AB AB, 
Apr, are received, as shown in Figure 4. The capital-