Suppose that you have the following bonds:

A: $1-$year zero coupon bond has a YTM of $2\mathrm{.}2\%$

B: $2-$year zero coupon bond has a YTM of $3\mathrm{.}0\%$

C: $3-$year zero coupon bond has a YTM of $3\mathrm{.}5\%$

a$.$ If each of these bonds has a face value of $$1000,$ what are the prices of each of these

bonds?

b$.$ What do bonds B and C imply about the interest rate in the third year?

c$.$ If the law of one price holds, what is the fair value of a $3-$year coupon bond with a

$10\%$ coupon and a face value of $$1000?$

d$.$ What is the duration of the $3-$year bond described in part c$?$

e$.$ What is the YTM of the $3-$year bond described in part c$?$