Problem 3 (25 marks) You are thinking of pursuing an actuarial career, so you have agreed to serve as an intern at Love Actuaries LLP.  The managing partner, Karen Thompson, has asked you to do some quick calculations for her. She wants you to use the current yield curve, flat at 6%, in your calculations.  Client Annie Inc. has a pension plan that pays pension benefits annually at a rate of $10 million per year, starting one year from today. The pension obligation will end in 40 years. Karen wants to know the duration of these required pension payments. Client Billy Mack Co. wants to immunize its pension obligations (present value = $150 million with a duration of 22 years) with two $1000 face value bonds. The first bond is a 7-year 5% annual coupon bond issued by Jaime Corp. The second bond issuer, Kari Ltd., has issued a consol bond paying a 10% annual coupon perpetually. Ms. Thompson wants you to calculate the money Billy Mack should allocate to each of these bonds to immunize its pension against interest rate risk. Thirdly, client Colin Limited’s pension plan obligation has a duration of 16 and a convexity of 29. Colin’s immunization strategy will use 3 bonds, issued by firms named Eleonore, Frissel, and Greta, respectively.    The bonds have the following parameters:  Bond   Duration   Convexity Eleonore     9.00   29.00 Frissel   21.00   35.00 Greta   28.00   56.00 Required:  What is the duration of Annie’s required pension payments? Hint: Starting with Spreadsheet 16.1 of Bodie_9Ce_Ch16.xlsx, copy the formulas for coupon bonds, adjusting them to extend for the full 40 years of payments, and determine the duration. Calculate the money Billy Mack should allocate to each of these bonds to immunize its pension against interest rate risk. (Again, modify Spreadsheet 16.1 for the coupon bond’s duration.) What weights should Ms. Thompson recommend for Colin’s strategy?