You are managing the portfolio for a university foundation that provides funding for research and scholarships. Your fund wants to provide $10 million of research and scholarships every year forever (e.g., in perpetuity) and that the discount rate associated with this investment is 7%. For simplicity, suppose you have the option of investing in a 30-year zero coupon bond and a 5-year coupon bond with a duration equal to 5 years. Show your work as needed for these 3 questions. 18. (4 pts.) What is the duration of your liabilities (e.g., the perpetual research and scholarship obligation) The formula for the duration of a perpetuity is: 1+r MacaulayDuration perpetuity where r = the discount rate. 19. (3 pts.) What is the duration of the zero-coupon bond? 20. (4 pts.) What percentage of your portfolio should be invested in the 30-year, zero-coupon bond if you want to immunize your portfolio from interest rate risk? You are managing the portfolio for a university foundation that provides funding for research and scholarships. Your fund wants to provide $10 million of research and scholarships every year forever (e.g., in perpetuity) and that the discount rate associated with this investment is 7%. For simplicity, suppose you have the option of investing in a 30-year zero coupon bond and a 5-year coupon bond with a duration equal to 5 years. Show your work as needed for these 3 questions. 18. (4 pts.) What is the duration of your liabilities (e.g., the perpetual research and scholarship obligation) The formula for the duration of a perpetuity is: 1+r MacaulayDuration perpetuity where r = the discount rate. 19. (3 pts.) What is the duration of the zero-coupon bond? 20. (4 pts.) What percentage of your portfolio should be invested in the 30-year, zero-coupon bond if you want to immunize your portfolio from interest rate risk