3. Consider a pension plan that will pay $10,000 once a year for a 5-year period (5 annual payments). The first payment will come in exactly 5 years (at the end of year 5) and the last payment in 9 years (at the end of year 9). a. What is the duration of the pension obligation? The current interest rate is 9% per year for all maturities. (3 marks) b. To generate the scheduled pension payments, the pension fund wants to invest the present value of the future payouts in bonds and match the duration of its obligation in part a). If the fund uses 5-year and 10-year zero-coupon bonds to construct its investment position, how much money (dollar amount) ought to be placed in each bond now? What should be the total face value (not current market value of each zero- coupon bond held? (3 marks) c. Right after the fund made its investment outlined in part b), market interest rates for all maturities dropped from 9% p.a.to 8% p.a. Show that the investment position constructed in part b) can still fund (approximately) the future payments by showing that the fund's net investment is close to 0 at the end of year 9 after making all the scheduled payments. Assume that interest rates will remain at 8% p.a. Any excess cash from the 5-year investment will be reinvested at 8% and any fraction of the 10- year bonds held can be sold at the going market price at any time to fund the annual payments. (6 marks) (Total for Question: 12 marks)