A life insurance company expects to pay the beneficiary of a policy $ 1,000,000 ten years from today. The manager of the company wants to make an investment today that will provide the necessary funding to make this payment. However, the manager also wants to immunize his firm against interest rate risk. The market yield is currently 7%. Suppose there are two fixed income securities available for investment: a 30-year 6% coupon bond and a 10-year 5% coupon bond. a) What combination of these two bonds would immunize the insurance company against interest rate risk and at the same time provide a value of approximately $1,000,000 ten years from today. b) Check whether this immunization works if the market interest rates immediately increase to 8% and stay at 8% for 10 years. (Take into account the facts that the 10-year bonds will expire in 10 years the 30-year bonds will be sold at 10 years, and that all coupon payments over the first 10 years will have to be reinvested.) A life insurance company expects to pay the beneficiary of a policy $ 1,000,000 ten years from today. The manager of the company wants to make an investment today that will provide the necessary funding to make this payment. However, the manager also wants to immunize his firm against interest rate risk. The market yield is currently 7%. Suppose there are two fixed income securities available for investment: a 30-year 6% coupon bond and a 10-year 5% coupon bond. a) What combination of these two bonds would immunize the insurance company against interest rate risk and at the same time provide a value of approximately $1,000,000 ten years from today. b) Check whether this immunization works if the market interest rates immediately increase to 8% and stay at 8% for 10 years. (Take into account the facts that the 10-year bonds will expire in 10 years the 30-year bonds will be sold at 10 years, and that all coupon payments over the first 10 years will have to be reinvested.)