Problem 3 (20 points) Your firm has an obligation to pay out $40,000 in 5 years and $210,000 in 7 years. You want to immianize this liability with zero-coupca bonds that have a matarity of 3 years and a perpetuity that makes annual payments. The current market interest rate is 6% a) Calculate the duration of the liability. b) What is the duration of the zero-coupon bond? What is the duration of the perpetuity? c) What proportions of your investment should you put into the zero-coupon bond and into the perpetuity to immunize your pouition? d) How much, in dollars, should you invest in each of the assets? e) What is the face value of your investment in the zero-coupon bond