Final answer:
The yield to maturity (YTM) of a bond is the internal rate of return on the bond's cash flows, and for a bond purchased at a premium, the YTM is slightly above the coupon rate. It takes into account all coupon payments and the face value. Exact calculation of YTM typically requires a financial calculator or appropriate formula involving the present value of annuity equation.
Step-by-step explanation:
To find the yield to maturity (YTM) of a 10-year bond with a coupon rate of 7% per annum (paid semi-annually) and a $1000 face value, sold at a price of $1050.74, we need to calculate the interest payments and the capital gains or losses over the bond's life. Since the bond pays interest semi-annually, the annual coupon payment of 7% totals to $70 per year, or $35 every six months. However, YTM calculation is more complex and typically requires a financial calculator or spreadsheet as it is the solution to the present value of annuity equation, which equates the present value of future cash flows (coupon payments and face value repayment) to the current price of the bond.
Using the formula or a financial calculator, we factor in the semi-annual payments and solve for the YTM, which essentially is the discount rate that makes the present value of all future cash flows equal to the bond's current price. It's important to note that while the coupon rate remains the same, market interest rates can affect the bond's price and therefore its yield. If the market interest rates rise, the price of existing bonds with lower coupon rates will decline, increasing their yield, and vice versa when interest rates fall.
For the bond in question, the YTM would typically be slightly above the coupon rate since the bond is purchased at a premium (above the face value). The exact YTM can be found using a financial calculator by entering the present price ($1050.74), the par value ($1000), the coupon payment ($35), and the number of periods until maturity (20 semi-annual periods for a 10-year bond), and then computing for YTM.