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1. An insurance company must make payments to a customer of $4 million in three years and $10 million in eight years. The market interest rate is 8% per year. a. What is the present value of the payments of the insurance company. Show your workings. (2 marks) b. Find the duration of the payments from the insurance company. Show your workings. (4 marks) c. Suppose the market interest rate falls by 0.5% point to 7.5%. Use the duration rule to estimate the dollar change in the present value of the payments of the insurance company. (3 marks) d. If the insurance company wants to immunize its obligation using a 6% annual coupon bond with the maturity of 3 years and with the face value of $1,000 and a perpetual bond paying annual coupons. Suppose the market interest rate is 8%. i. Find the Macaulay Duration of the annual coupon bond. Show your workings. (4 marks) ii. Determine the weight of the annual coupon bond and the perpetual bond to immunize its payments. Show your steps clearly. (5 marks) iii. How much should be invested in each of the bonds? Show your calculations. (2 marks)