For a bond issue which sells for less than its face amount, the market rate of interest is higher than the rate stated on the bond.
Bonds can be sold for more and less than their par values because their interest rates change depending upon the market conditions. Like most fixed-income securities, bonds are highly correlated to interest rates. Thus, when interest rates go up, a bond's market price will fall and vice versa.
The actual market value of a bond may not be reliably as indicated by its face value because there are many other influencing forces at play, such as supply and demand in the market.
Hence, when the price of a bond goes above its face value, it is said to be a premium bond, and when the price is below its face value, it is known as a discount bond.
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