Am stuck in finding solutions for this problem

The 1-year spot rate is 4.1%pa. The 2-year spot rate is 4.0% pa. The 4-year spot rate is 4.4% pa. The 5-year spot rate is 4.5% pa. (i) Calculate the theoretical price of a 3-year zero-coupon bond that is issued at time 2 and is redeemable at par. [2] (ii) A 1-year zero-coupon bond is issued at time 3 and has a theoretical price of $95.50 per E100 nominal. Given that the bond is redeemable at par, calculate: (a) the 3-year spot rate, and (b) the 1-year forward rate starting at time 2. [3] (iii) Calculate the gross redemption yield on a bond that pays annual coupons of 6% pa (at times 1, 2, 3, 4 and 5) and is redeemable at 1 10% in 5 years' time. [4] [Total 9]An insurance company has liabilities of E10 million due in 10 years time and $20 million due in 15 years time, and assets consisting of two zero-coupon bonds, one paying $7.404 million in 2 years time and the other paying $31.834 million in 25 years time. The current interest rate is 7% per annum effective. (i) Show that Redington's first two conditions for immunisation against small changes in the rate of interest are satisfied for this insurance company. [5] (ii) Determine the profit or loss, expressed as a present value, that the insurance company will make if the interest rate increases immediately to 7.5% per annum effective. [2] (iii) Explain how you might have anticipated, before making the calculation in (ii), whether the result would be a profit or loss. [2] [Total 9]An individual purchases (100,000 nominal of a bond on 1 January 2003 which is redeemable at 105% in four years time and pays coupons of 4% per annum at the end of each year. The investment manager wishes to invest the coupon payments on deposit until the bond is redeemed. It is assumed that the rate of interest at which the coupon payments can be invested is a random variable and the rate of interest in any one year is independent of that in any other year. Deriving the necessary formulae, calculate the mean value of the total accumulated investment on 31 December 2006 if the annual effective rate of interest has an expected value of 519% in 2004, 6% in 2005 and 42 % in 2006. [5]