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= Assume that the 1-year zero-coupon rate is currently ro =0.35% and that it evolves over time according to the following process: r4+1 = r + 0.15(2% - r). Assume further that the current n-year zero coupon rate rin satisfies the following relationship for n > 2, nrin = x= ri + 0.07xDuration(n), where Duration (n) is the durations of an n-year zero coupon bond. That is, the current 2-year rate r satisfies the relation: 2r2 ro +r1 + 0.07 Duration(2); the current 3-year rate r satisfies the relation: - 3r3 = r +r1 +r2 + 0.07Duration(3); and so on. I a. What is the price of a 4-year coupon bond with a coupon rate of 2% paid once at the end of the year and with a par value of $100? What is this bond's duration?| b. What is the Treasury futures rate for a 2-year contract that starts in 2 years? c. An institutional investor currently holds five of the 4-year, 2% coupon bonds, each with a par vale of $100.. She wishes to sell off (borrow) a number of 2-year zero coupon bonds such that the Duration of her overall portfolio is zero-a process known as immunization. How many 2-year, zero coupon bonds must she sell to achieve her goal? = Assume that the 1-year zero-coupon rate is currently ro =0.35% and that it evolves over time according to the following process: r4+1 = r + 0.15(2% - r). Assume further that the current n-year zero coupon rate rin satisfies the following relationship for n > 2, nrin = x= ri + 0.07xDuration(n), where Duration (n) is the durations of an n-year zero coupon bond. That is, the current 2-year rate r satisfies the relation: 2r2 ro +r1 + 0.07 Duration(2); the current 3-year rate r satisfies the relation: - 3r3 = r +r1 +r2 + 0.07Duration(3); and so on. I a. What is the price of a 4-year coupon bond with a coupon rate of 2% paid once at the end of the year and with a par value of $100? What is this bond's duration?| b. What is the Treasury futures rate for a 2-year contract that starts in 2 years? c. An institutional investor currently holds five of the 4-year, 2% coupon bonds, each with a par vale of $100.. She wishes to sell off (borrow) a number of 2-year zero coupon bonds such that the Duration of her overall portfolio is zero-a process known as immunization. How many 2-year, zero coupon bonds must she sell to achieve her goal

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