3. An investor has short position valued at $100 in a 1-year, zero coupon T-Bill with a 7% discounting rate. Assume discounting occurs annually. Now consider the case that the discounting rate increase 50bps, calculate the dollar duration? (hint: calculate the price of bond before and after the change of discounting rate). Using a 1-year bond (hedge instrument) with a dollar duration of 40 to hedge the interest rate of the 1-year T-bill above. Calculate the total amount of bond you need.Should you buy or sell the hedge instrument? 3. An investor has short position valued at $100 in a 1-year, zero coupon T-Bill with a 7% discounting rate. Assume discounting occurs annually. Now consider the case that the discounting rate increase 50bps, calculate the dollar duration? (hint: calculate the price of bond before and after the change of discounting rate). Using a 1-year bond (hedge instrument) with a dollar duration of 40 to hedge the interest rate of the 1-year T-bill above. Calculate the total amount of bond you need.Should you buy or sell the hedge instrument