212 NATURE OF CAPITAL AND INCOME [Caar. XIII

per cent, ten-year, $100 bond ”’ means the right to receive
an annuity of $5 a year for ten years, and, in addition,
$100 at the end of the ten years.
If the rate of interest is five per cent, and one buys a bond
which entitles him to an annual income of $5 a year for ten
years and $100 returnable at the end of this period, it is
evident that the purchase price of the bond must be $100.
In this case the $5 of annual income is the interest on the
purchase price, and the sum of $100 which is to be received
at maturity is equal to the originally invested capital or
“principal.” For these reasons such a bond is called a five
per cent bond, the annual installments of income are called
“interest,” and the final payment of $100 is called “principal.”

But more often than not the bond is not sold at par; consequently
 all of the three terms just mentioned are misnomers.
 If the bond is sold above par the rate of interest
is not five per cent, but less than five per cent, so that it is
only nominally a “five per cent bond”; the $5 annually
received is only nominally “ interest’; and the $100 returnable
 at the end is only nominally “ principal.”
In order to obtain the capital-value of a so-called five
per cent bond when the market rate of interest is four per
cent (i.e. when the bond is sold on a four per cent basis),
we need simply to add together the present values (reckoned
at four per cent) of the ten payments of $5 and of the final
payment of $100. We may consider these items as consisting
 of (1) a ten-year annuity of $5 a year, and (2) a sum of
$100 deferred ten years. Both of these we can easily find
from the explanations already given.
It has been explained® that the present value of a tenyear
 annuity is the “total discount” on the capitalized
value of a corresponding perpetual annuity beginning when
the terminable annuity ceases. Now a perpetual annuity
of $5 is worth, if interest is four per cent, 5, or $125.2

1 See § 5, supra. 2 See § 3, supra.