Final answer:
To determine the price of the bond when the interest rate is 8%, calculate the present value of the bond's cash flows. Using the present value formula, the price to guarantee an interest rate of 8% is $875.47 (option A).
Step-by-step explanation:
To determine the price of the bond when the interest rate is 8%, we need to calculate the present value of the bond's cash flows. The bond pays a coupon of 9% on a par value of $1,000 for the first 10 years, and then a coupon of 8% for the remaining 10 years.
At the end of 20 years, the bond matures and is redeemed at par. However, the bond is callable at the end of year 10 at $1,100 and at the end of year 15 at $1,050.
To calculate the bond's price at an interest rate of 8%, we can use the present value formula:
PV = C1 / (1+r)^1 + C2 / (1+r)^2 + ... + Cn / (1+r)^n + F / (1+r)^n
Where PV is the present value, C1, C2, ..., Cn are the cash flows, r is the interest rate, and F is the face value or redemption value of the bond. We substitute the values and calculate the present value.
Using the present value formula, the price to guarantee an interest rate of 8% is $875.47 (option A).