Final answer:
The price of a bond is calculated by discounting the future cash flows, which include semi-annual coupon payments and the face value at maturity, by the bond's yield to maturity. For bonds with semi-annual coupons and changes in yield to maturity, adjustments in price reflect the current value of these cash flows at the new rate.
Step-by-step explanation:
To determine the price of a bond, we need to calculate the present value of its future cash flows, which include the semi-annual coupon payments and the face value repaid at maturity. The discount rate used for these cash flows corresponds to the bond's yield to maturity (YTM). For the first bond mentioned, the YTM is 7.7% APR, compounded semi-annually, with a 7.1% coupon rate and two years to maturity. However, the resulting price in the question appears to be a placeholder, as no calculation is provided.
For the second bond with a 10-year maturity, coupon rate of 8.9%, and a semi-annual payment structure trading at $1,034.76, a change in YTM to 9.2% would mean the present value of the bond's cash flows must be recalculated using this new rate. An increase in YTM generally leads to a decrease in the bond's price, because the fixed coupon payments and the face value are discounted by a higher rate, resulting in a lower present value.
Remember, when interest rates rise, the price of existing bonds with lower rates fall, as investors can find new bonds with more attractive yields. Conversely, when interest rates fall, prices of existing bonds with higher coupon rates increase, as they become more desirable since they offer higher returns than newly issued bonds.