Final answer:
To calculate the maximum price for a bond with known coupon rate and yield to maturity, one must discount future payments including semiannual coupons and the face value at the yield to maturity and sum these discounted values.
Step-by-step explanation:
The student is asking how to calculate the maximum price one should be willing to pay for a bond with a 9.5% annual coupon rate, a face value of $1,000, that makes semiannual interest payments, given a required nominal yield to maturity of 11.0%.
First, we need to determine the semiannual interest payment: this would be 9.5% of $1,000 divided by two, which is $47.50 per period. Since the bond makes these payments semiannually for 15 years, there will be 30 payments. To find the present value of these interest payments, we need to discount them at the investor's required yield to maturity, which in this case is also semiannual (11.0% per annum or 5.5% per period).
Next, we also discount the face value of $1,000 which will be received at the end of the 15 years. By summing the present discounted value of the series of interest payments and the discounted face value, we get the maximum price the investor should be willing to pay for the bond.