My pension plan will pay me $$10,000$ once a year for a $10-$year period. The first payment will come in exactly five 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?

c$.$ What will be the face value of the holdings in each zero?