Final answer:
The yield to maturity (YTM) of a bond is determined by equating the present value of expected future cash flows to its current market price and solving for the yield. Semiannual coupons add complexity, requiring iterative solutions or financial calculators.
Step-by-step explanation:
To find the yield to maturity (YTM) of a bond with semiannual coupons, one needs to solve for the interest rate (y) in the bond's present value equation that equates the present value of expected future cash flows to its current market price. The equation considering semiannual periods is:
PV = C * (1 - (1 + y)^(-n)) / y + F / (1 + y)^n
Where PV is the current market price ($957.35), C is the semiannual coupon payment ($50, since it's a 5% annual rate paid semiannually on a $1000 face value bond), n is the number of periods (10, because it's 5 years with semiannual payments), and F is the face value ($1000).
This equation does not lend itself to direct calculation and must be solved using financial calculators, spreadsheet software, or iterative methods such as the Newton-Raphson method.
Because YTM calculators are commonly used for this purpose, providing a calculated YTM isn't possible without the actual calculations, but it's typically found to be slightly higher than the coupon rate when the bond is bought at a discount.