This section is from the "Why Bonds Are Safe Investments" book, by Harris Trust & Savings Bank. Also see Amazon: Why Bonds Are Safe Investments.
The price of a bond like the price of grain, provisions or any other commodity, depends upon market conditions existing at the time. Naturally, other things being equal, a six per cent bond will bring a higher price than a five per cent bond, because the income of the six per cent bond is greater. But the security behind the five per cent bond may be so much greater than that behind the six per cent bond that the five per cent bond, will be more attractive, therefore in greater demand and commanding a higher market price. Also the question whether the interest from the bond is subject to the income tax, affects its price. For example, municipal bonds being free from federal income taxes (See page 19) command a higher price for this reason as well as for their high degree of security. Besides these considerations there is the general question of the prevailing price of money in the markets of the world; in other words, general interest rates. Thus, these influences taken together may cause a bond to sell for more or less than its face value, or for exactly that amount (par). That is, one kind of a $1,000 bond may be so attractive that it may sell for $1,080; or as the price would be quoted in percentage, at 108 (at eight per cent premium, or eight per cent above par). Another $ 1,000 bond may be, for entirely legitimate reasons, less in demand and sell for $900; or in market terms, at 90 (at ten per cent discount, or ten per cent below par).
There may be a marked difference between the rate of interest paid and the rate of income on the investment in a bond. The rate of interest on any given bond is the same, but the rate of income which the investor receives from his investment in a bond varies according to the price paid, the interest rate specified and the length of time the bond has to run.
When a bond is sold below its face, or par, value, in other words at a discount, the rate of income is naturally more than the fixed rate of interest named in the bond, because the interest is figured on the face value and the investor has not paid the full face value for the bond. On the contrary, when a bond is sold at a premium, or above its face value, the rate of income derived from the investment naturally is less than the rate of interest named in the bond. While the interest on a $1,000 six per cent bond is always $60 a year, the actual percentage of yield or income to the investor is more than six per cent or less than six per cent according as the price paid for the bond is at a discount or a premium.
If a bond is bought at a price below its face value, say 97 for a 6% bond of $100 face value, maturing in three years, not only does the investor receive slightly more than 6%, because $ 6.00 amounts to a little more than six per cent on $ 97, but also at the end of three years, when the bond is paid at 100, he gains the difference between $ 97 and $ 100, and this amount ($ 3.00) is included in the "yield" on the investment. It must of course be spread out over the period of the investment and in this example it makes the yield over 7% (approximately 7.12%).
Standard tables of figures have been prepared by mathematicians and actuaries for use in such transactions which show what is earned on a given bond at a given price. These tables take into consideration the principle of compound interest and involve rather complicated mathematical computations, but the example given in the preceding paragraph serves to illustrate the general principle.
Main Banking Room, Harris Trust & Savings Bank.
 
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