12. (Bond selection) Consider the four bonds having annual payments as shown in Table 3 9 They are traded to produce a 15% yield (a) Determine the price of each bond (b) Determine the duration of each bond (not the modified duration) (c) Which bond is most sensitive to a change in yicld? (d) Suppose you owe $2,000 at the end of 2 years Concern about interest rate risk sug- gests hat a portlolio consisting of the bonds and the obligation should be immunized If VA, Vu, Vc, and VD are the total values of bonds purchased of types A, B, C, and D, respectively, wiat are the necessary constraints to implement the immunization? (Hint Ihere are two equations (Do not solve )] TABLE 3.9 End of year paymentsBond A Bond B Bond CBond D Yeai l Yeai 2 Year 3 100 100 100 + 100050 10000+ 1000 0 50 50 0 0 0 + 1000 0