There are two types of bonds available in the market: a 4-year bond A with annually paid coupon rate of 30% selling at a yield to maturity of 30%. and a 4-year zero-coupon bond B selling at a yield to maturity of 30%. Both types have a par value of $1,000 and assume that the number of the bonds can be sold in proportional to the dollar amounts invested. Answer the following questions based on the information above. No points are given without showing calculation steps or giving detailed explanation. 

 a.    What is the duration for the 4-year coupon bond A? 

b.    Suppose that you want to choose either bond A or bond B, to invest for 3 years. If you expect that the discount rate may be 25% for the following five years after your purchase, which bond is a better investment choice? Compare their effective annualized returns. 

c.    Suppose that you now manage a pension fund for $1,000 that will provide retired workers a guaranteed investment contract (GIC) with 3-year maturity, and a guaranteed interest rate of 30%. As you expect that there will be uncertainty in the future discount rate, how do you invest in bond A and/or bond B to fund and immunize the obligation? Assume that the discount rate is 35% for the following five years after your investment, validate the immunization by comparing the accumulated value of your investment with your obligation at maturity.