13. My pension plan will pay me $10,000 once a year for a 10-year period. The first payment will come in exactly 5 years. The pension fund wants to immunize its position.

a. What is the duration of its obligation to me? The current interest rate is 10% per year.

b. If the plan uses 5-year and 20-year zero-coupon bonds to construct the immunized position, how much money ought to be placed in each bond? What will be the face value of the holdings in each zero?