(a) Consider a 17-year, 7.5% corporate bond with face value $1,000. Assume that the bond pays semi-annual coupons. Compute the fair value of the bond today if the nominal yield-to-maturity is 12.78% compounded semi-annually. (b) Consider a company called Human Intelligence Inc. (HII), which has issued two different zero-coupon bonds. The first bond is a 4-year bond with a face value of $10,000 issued three years ago. The second bond is a 3-year bond with a face value of $1,000 issued two years ago. Note that both bonds are zero-coupon bonds and have exactly one year to maturity. Note that HII, being a public corporation, can default. If HII defaults, the recovery rate times the bond's face value will be paid in one year for each of these two bonds. If HII does not default, the full face value will be paid in one year. Assume that the recovery rate for the first and the second bonds are 80% and 60%, respectively. Assume that the effective 1-year risk-free rate is 5%.

(i) If the first bond is trading at $9,238.10, find the risk-neutral probability that the HII will default within one year.

(ii) Find the fair value of the second bond.