a. Suppose a three-year corporate bond provides a coupon of 10% per year payable semi-annually and has a yield of 8% per annum (expressed with semi-annual compounding). The yields for all maturities on risk-free bonds are 4% per annum (expressed with semi-annual compounding). Assume that defaults can take place at the end of each year (immediately before a coupon payment) and recovery rate is 45%. Estimate the default probabilities assuming the unconditional default probabilities are the same on each possible default date.