Final answer:
A seven-year $1,000 bond with an 8.4% coupon rate and semiannual coupons trading at a YTM of 6.38% would be at a premium. If the YTM rises to 7.08%, the bond would still trade at a premium, albeit a smaller one. The exact new price requires present value calculations for each future cash flow.
Step-by-step explanation:
When given a seven-year, $1,000 bond with an 8.4% coupon rate and semiannual coupons that is trading with a yield to maturity (YTM) of 6.38%, the bond would be trading at a premium. This is because the bond's coupon rate is higher than the current yield to maturity, meaning it offers more periodic returns in the form of coupons than required by the current market rate. As a result, the price is bid up above par value.
If the yield to maturity rises to 7.08% with semiannual compounding, to calculate the new trading price of the bond, you must discount the bond's future cash flows - which include semiannual coupon payments and the face value to be received at maturity - at the new YTM rate. Since the new YTM is closer to the bond's coupon rate but still lower, the bond would still trade at a premium but less so than before. The actual calculation would be more intricate and requires the present value formula for each cash flow.