8. (20 points) Assume a flat yield (and zero) curve of 2 3.4%. A pension fund manager has the following obligations to pay in the future: i. $10mn in 5 years' time ii. $10mn in 10 years' time iii. $20mn in 15 years' time For what follows, use annual discounting and round answers to the nearest hundredth (cent or basis point). (a) (5 points) What is the present value of liabilities? (b) (5 points) What is the Macaulay duration of liabilities? (c) (10 points) Assume the pension plan is fully funded in that the manager has cash on hand equal to the present value of liabilities. The manager has already decided to purchase a zero-coupon bond with 5 years to maturity and a face value of $15mn. The manager plans on investing the rest into another zero- coupon bond. What maturity would you recommend? (I am looking for a specific number) Explain why