*Show all step of calculation and detail

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.

i) What is the duration for the 4-year coupon bond A?

ii) 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 35% for the following five years after your purchase, which bond is a better investment choice? Compare their effective annualized returns.

iii) 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.

iv) 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.