You manage a $100million bond portfolio (actual, current value) with a modified duration of 8.You're worried about future Federal Reserve policy and you want to use interest rate options to protect your portfolio from a potential increase in rates of a half a percent before you sell your portfolio.The current 'at the money' (strike = current rate) call option on 20-year bonds with a yield of 5% have a premium of 2.How many option contracts should you buy to protect yourself against this potential interest rate increase?What is the cost of this 'insurance policy'?How is using interest rate options different from using interest rate futures in an uncertain interest rate environment?Show all work.