An insurance company has liabilities of 6 million due in 8 years' time and 11 million due in 15 years' time. The assets consist of two zero-coupon bonds, one paying X in 5 years' time and the other paying Y in 20 years' time. The current interest rate is 8% per annum effective. (i) Find the values of X and Y such that the first two conditions for immunisation against small changes in the rate of interest are satisfied. [7 marks] (ii) Explain clearly whether or not the third condition required for immunisation will also be satisfied in this case. [2 marks] (iii) Give 2 reasons why, in general, immunisation is difficult to achieve in practice. [2 marks] [Total 11 marks] An insurance company has liabilities of 6 million due in 8 years' time and 11 million due in 15 years' time. The assets consist of two zero-coupon bonds, one paying X in 5 years' time and the other paying Y in 20 years' time. The current interest rate is 8% per annum effective. (i) Find the values of X and Y such that the first two conditions for immunisation against small changes in the rate of interest are satisfied. [7 marks] (ii) Explain clearly whether or not the third condition required for immunisation will also be satisfied in this case. [2 marks] (iii) Give 2 reasons why, in general, immunisation is difficult to achieve in practice. [2 marks] [Total 11 marks]