Final answer:
The question is about calculating the Effective Annual Yield (EAY) for a bond with semiannual coupon payments. It involves determining the internal rate of return (IRR) for the semiannual periods and then adjusting for compounding to find the EAY.
Step-by-step explanation:
The student is asking about the Effective Annual Yield (EAY) to maturity on a bond that Huan Zhang bought. The bond has a coupon rate of 8%, a face value of $1,000, and the payments are semiannual. Huan paid $1,015.10 for the bond, and it matures in 7 years. To calculate the EAY, we need to find the internal rate of return (IRR) for the bond's cash flows and adjust it for semiannual compounding.
To begin, we note that the semiannual coupon payment is 4% of the $1,000 face value (since 8% per year divided by two semiannual periods is 4%), which equals $40. Since there are 14 semiannual periods in 7 years, Huan will receive $40 every six months. At maturity, he will also receive the $1,000 face value of the bond. Using a financial calculator or spreadsheet, we input these cash flows and solve for the yield per semiannual period. After we obtain the semiannual yield, we calculate the EAY by using the following formula:
EAY = (1 + semiannual yield)2 - 1.
This calculation will provide the effective annual yield, which is the actual interest rate earned over a year, taking into account the effect of compounding. Calculating the exact EAY would require a financial calculator or numerical methods because it involves solving for the IRR, which is not a straightforward calculation that can be done manually.