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 milion in 25 years' time. The current interest rate is 7% per annum effective. c) Show that Redington's first two conditions for immunisation against small changes in the rate of interest are satisfied for this insurance company [6] 0 Calculate the present value of profit that the insurance company will make the interest rate increases immediately to 7.5% per annum effective [21 3) Explain without any furher calculation, why the insurance company made a profit as a result of the change in the interest rate. [2] [Total 101