You have been hired as an intern at a major investment firm. Since you are well known for your meticulous analysis, your superior gives you a set of investment to analyze. Here are the details:

A. Government risk-free bond with a face value of $1,000 that mature in 5 years with annual coupons of 4%. Its risk rating by Standard's and Poor's is AAA

B. Corporate bond with a face value of $1,000 that matures in 4 years with annual coupons of 6% and yield to maturity of 5%. Its risk rating by Standard's and Poor's is AA

C. A zero-coupon bond with a face value of $1,000 that matures in one year with a yield to maturity of 6.5 %. Its risk rating by Standard's and Poor's is CC.

You are also given with certainty that the risk-free rates are t1= 1.00%, .50%, t3= 1.75%, %, t5= 2.25%.

a. For each product, what is the purchase price?

b. The issuer of the zero-coupon bond told you that there is half probability that it only repay back $700 to the investors. What is the yield to maturity and the expected return on that bond?