Final answer:
To find the price of the bond, we need to calculate the present value of its future cash flows. The cash flows include the coupon payments and the face value of the bond. The present value of the bond is approximately $751.31.
Step-by-step explanation:
To find the price of the bond, we need to calculate the present value of its future cash flows. The cash flows include the coupon payments and the face value of the bond.
Step 1: Calculate the semi-annual coupon payment. The coupon rate is 5% of the face value, so the semi-annual coupon payment is $1,000 * 5% / 2 = $25.
Step 2: Calculate the number of semi-annual coupon payments over the life of the bond. Since the bond matures in 11 years, there are 11 years * 2 = 22 semi-annual periods.
Step 3: Use the present value formula to calculate the present value of the bond. The formula is:
PV = C * [1 - (1 + r)^(-n)] / r + F / (1 + r)^n
Where:
- PV is the present value of the bond
- C is the coupon payment
- r is the discount rate (market-determined discount rate)
- n is the number of coupon payments
- F is the face value of the bond
Plugging in the values:
- C = $25
- r = 10% / 2 = 5% (since the discount rate is semi-annual)
- n = 22
- F = $1,000
Using a financial calculator or spreadsheet, we can calculate that the present value of the bond is approximately $751.31.
Therefore, the price of the bond is approximately $751.31.