Il. (Immunization, 20 points) In Smallville, there are only two bonds that always have the same yield. Bond 1 is a 30-year (maturity), 8% (of face value per year, coupon rate, paid twice a year) bond, with a face value of $100. Bond 2 is a 10-year, 12% bond, with a face value of 5100. Moreover, the yield of the bonds is utilized as the base interest rate in Smallville. The current yield (interest) is 10% (per year, compounded semiannually). When demand in the market increases, the prices of bonds increase, and the yield (the interest) drops, and vice versa. People who buy bonds today are concerned that the interest rate could increase tomorrow, and decrease their investment value. In particular, the X2 corporation is considering investing in a portfolio of the two bonds to meet a future obligation of $500,000 after 8 years from now. (a) Find the prices of Bonds 1 and 2. (b) Find the Macaulay durations of Bonds 1 and 2. (c) Structure a Bond portfolio that allows X2 to meet its obligation while hedging interest risk