Sec. 7] VALUE OF CAPITAL 213
A perpetual annuity beginning in ten years will thus be
worth $125 —in ten years. To-day, therefore, it is worth,
by discounting at four per cent, gam or $84.45. The
“ total discount” is, therefore, $125 less $84.45, or $40.55.
We need to add to this the other element in the bond,
namely, the present value of the so-called “principal” of
$100 due in ten years. Discounted at four per cent, this
is worth i%s, or $67.56. Combining our two figures we
have, for the value of the bond, $40.55 + $67.56, or $108.11.
We find, therefore, that a so-called five per cent bond
yields the investor four per cent if it is bought at $1084.
In like manner it could be shown that it will yield him six
per cent, if bought at $92.50." ;
In general a bond sells at par when the annual income,
or nominal “interest,” is equal to the true interest on the
principal ; it sells above par if the annual income (nominal
interest) is greater than the interest on the principal; and
below par if it is less.
In a similar way we may calculate the value of a bond in
cases where the installments of income, or nominal interest,
are semi-annual and the rate of interest is reckoned semiannually,
and in the case of more frequent intervals, as well
as in the limiting case of continuous payment.”
Elaborate tables have been constructed, called “bond
value books,” calculated on the foregoing principles, which
are used by brokers for showing the value of bonds under
different circumstances. The tables are usually employed,
however, for the converse problem, to find the rate of interest
“realized” when a bond is bought at a given price.
The following is an abridgment of these tables, for (socalled)
three per cent, four per cent, and five per cent bonds.
The prices of the bonds in all cases are the prices taken
ment, see Appendix to Chap. XIII,
leulating the value of a bond
separately, see Appendix to
1 For a mathematical state
§ 8; for an alternative method of ca
and one which gives the “premium ”’
Chap. XIII, § 9.
? For mathematical statement, see Appendix to Chap. XIII, § 10.
