Liabilities at times 3 and 5 of amounts 3000 and 1000 , respectively, are to be immunized with 2-year and 8-year zero coupon bonds. Assume a flat yield curve of 3%. (a) Determine the cost to immunize the liabilities. (b) Determine the asset amounts at time 2 and at time 8 that are needed in order for the first two conditions of immunization to be satisfied. (c) If the zero coupon bonds are 1000 face value bonds, redeemable at par, then how many of each type of bond should be purchased in order to immunize the liabilities. (Assume we can buy any number (even fractions) of bonds.) (d) Given immunization as above, determine the excess of the present value of assets over the present value of liabilities if the interest rate is changed to 6% annual effective, and then determine the excess of the present value of assets over the present value of liabilities if the interest rate is changed to 1% annual effective