Kindly provide accurate answers to the following assignments

An insurance company has liabilities of f10 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](a) Explain what is meant by the "expectations theory" explanation for the shape of the yield curve. (b) Explain how expectations theory can be modified by both "liquidity preference" and "market segmentation" theories. [6] Short-term, one-year annual effective interest rates are currently 10%; they are expected to be 9% in one year's time, 8% in two years' time, 7% in three years' time and to remain at that level thereafter indefinitely. (a) If bond yields over all terms to maturity are assumed only to reflect expectations of future short-term interest rates, calculate the gross redemption yields from 1-year, 3-year, 5-year and 10-year zero coupon bonds. (b) Draw a rough plot of the yield curve for zero coupon bonds using the data from part (ii)(a). (Graph paper is not required.) (c) Explain why the gross redemption yield curve for coupon paying bonds will slope down with a less steep gradient than the zero coupon bond yield curve. [8]