A risky company issues a one-year corporate bond. The market believes that there is a 4% chance that bondholders will receive nothing, a 7% chance that they will receive $500 of the $1000 principal and no interest, and in the remaining cases they will be paid in full. What promised rate should this bond pay, given a treasury risk-free rate of 3% and that it sells at par? (assume investors are risk-neutral)

.b) If you know that the bond sells at $1005 and that the probabilities of payment in full and of receiving nothing are the same as in part a), what is the amount the market believes bondholders will receive should the bond default, but there will be recovery (7% probability).