please show work

3. Consider the following 3 risk-free bonds, all with face amounts of $1,000: (i) a 1-year zero-coupon bond, (ii) a 2-year bond with a coupon rate of 6% annual coupons), and (iii) a 2-year zero-coupon bond, all with yields of 6%. a. What are the Macaulay durations of these 3 bonds? What are the modified durations? b. If the yields on all 3 bonds rise immediately to 7%, what does the duration predict will be the percentage change in the bond price? What is the actual percentage change in the bond price? c. At the original yield of 6%, what positions in the 2 zero-coupon bonds would you take to immunize a long position of $1,000 in the 2-year bond? What is the change in the value of this immunized portfolio if the yields on all the bonds rise immediately to 7%? TI tai