Final answer:
A seven-year, $1,000 bond with a 7.7% coupon rate is trading at a premium when the yield to maturity is 6.42%. If the yield to maturity rises to 7.08%, the bond's price will decrease and may trade at or below face value, as the fixed coupon payments become less attractive given the higher prevailing interest rates.
Step-by-step explanation:
If a seven-year, $1,000 bond with a 7.7% coupon rate and semi-annual coupons is trading with a yield to maturity of 6.42%, it means that the required rate of return from investors is below the coupon rate. Thus, investors are willing to pay more for the bond than its face value, so the bond is currently trading at a premium. This occurs because the coupon payments are more attractive compared to the lower yield currently required by the market.
When the yield to maturity of the bond rises to 7.08%, the bond price will adjust downwards. This is because the fixed coupon payments become less attractive compared to the new, higher available market yields, and so the bond must be sold at a discount to attract buyers. To calculate the bond price accurately, one would need to use the bond pricing formula, which takes into account the present value of the coupon payments and the face value, all discounted at the new yield to maturity.