Hi, I am reposting this for the second time without help.

1 The n-year spot rate is estimated using the function y, =0.09-0.030 0." . Calculate the one-year forward rate at time 10. 2 Let f denote the 1-year forward rate for a transaction beginning at time t . Calculate the 3-year par yield, given that: fo =6%, f1 =6.5%, f2 =7% 3 In a particular bond market, the two-year par yield at time t =0 is 5.65% and the issue price at yle time t=0 of a two-year fixed-interest stock, paying coupons of 7% annually in arrears and redeemed at 101, is E103.40 per E100 nominal. Calculate: (a) the one-year spot rate (b) the two-year spot rate. [6] 4 Three bonds each paying annual coupons in arrears of 6% and redeemable at (103 per E100 yle nominal reach their redemption dates in exactly one, two and three years' time, respectively. The price of each bond is $97 per E100 nominal. Calculate the gross redemption yield of the 3-year bond. [3] Calculate the one-year and two-year spot rates implied by the information given. [3] [Total 6]8 A company has to pay f 2,000(10-t ) at the end of year t , for t =5,6,7,8,9. It values these yle liabilities assuming that there will be a constant effective annual rate of interest of 6% pa. (i) Calculate the present value of the company's liabilities. [3] The company wants to immunise its exposure to the liabilities by investing in two bonds: Bond A pays coupons of 5% po annually in arrears and is redeemable at par in 15 years' time Bond B is a zero-coupon bond that is redeemable at par in 5 years' time. The gross redemption yield on both stocks is the same as the interest rate used to value the liabilities. (1i) (a) Determine the amount that the company should invest in each of the two bonds to ensure that the present value and discounted mean term of the assets are equal to those of the liabilities. (b) State the third condition required for immunisation. [9] [Total 12] 9 An insurance company has liabilities of $10 million due in 10 years' time and $20 million due in 15 years' time. The company's assets consist of two zero-coupon bonds. One pays $7.404 million in 2 years' time and the other pays $31.834 million in 25 years' time. The current interest rate is 7% per annum effective. Show that Redington's first two conditions for immunisation against small changes in the rate of interest are satisfied for this insurance company. [6] Calculate the present value of profit that the insurance company will make if the interest rate increases immediately to 7.5% per annum effective. [2] (iii) Explain, without any further calculation, why the insurance company made a profit as a result of the change in the interest rate. [2] [Total 10]