A pension plan will pay me $10,000$ once a year for a $10-$year period. The first payment will come in exactly $1$ year. The pension fund wants to immunize its position:

$($i$)$ What is the duration of its obligation to me$?$ The current interest rate is $10\%$ per year

$($ii$)$ If the pension fund would like to use the $5-$year zero coupon bond to immunise its position. Will it buy or sell the zero coupon bond and how much is the size of the zero coupon bond?