Bond A$,$ a two$-$year, twelve percent coupon issue can be purchased for $$957\mathrm{.}9920.$ Bond B$,$ a twoyear, five percent coupon issue can be purchased for $$840\mathrm{.}2471.$

a$)$ What would be the value of a $$1000$ face value pure discount bond maturing in two years?

$($Hint: complete part b first$)2$ marks.

b$)$ The two$-$year pure discount bond can be replicated with a portfolio comprised of bonds A

and B$.$ What should the portfolio weights of these bonds be$?($Short selling is permitted.$)$

$4$ marks

c$)$ I need to raise $$15,000$ at the end of year one and $$12,000$ at the end of year two to repay

some debts. How much should I buy $($sell$)$ of each of Bonds A and B to exactly match my

debt payments? $3$ marks

d$)$ What is the duration of the bond in part d$?1$ mark