Final answer:
A bond with a yield to maturity less than its coupon rate sells at a premium, but if market interest rates increase, the premium decreases. Rising rates lead older bonds to sell at a discount, while falling rates make older, higher-coupon bonds sell at a premium. In a situation with increased interest rates, you would pay less than the bond's face value.
Step-by-step explanation:
If a bond's yield to maturity is less than its coupon rate, the bond will sell at a premium; and if market interest rates increase, this will decrease the premium. When the market interest rates rise, newly issued bonds come with higher coupon rates, making older bonds with lower rates less attractive.
As a result, the less attractive bonds sell at a discount to entice investors. Conversely, when market rates fall, older bonds with higher rates become more desirable, leading these bonds to trade at a premium.
Given a change in market interest rates, if you possess a bond and its coupon rate is higher than current market rates, you can expect to sell it for more than its face value, or at a premium. If the market rates are higher than your bond's coupon rate, it will sell for less than the face value, or at a discount.
For example, if the bond's face value is $1,000, with a coupon rate of 8%, and market rates rise to 12%, an investor would have to reduce the selling price to make the bond's yield to maturity attractive. Therefore, one would expect to pay less than $1,000 for such a bond in a higher interest rate environment.