Question $2-$Consider a bond that has a life of $2$ years and

pays a coupon of $10\%$ per annum $($with semiannual payments$)$; the yield is $5\%$ per annum with semiannual compounding.

$($a$)$ What is the bond's price?

$($b$)$ What is the bond's duration?

$($c$)$ Suppose that the bond price is the one you computed in part $($a$)$ and that the $6M,12M,$ and $18M$ zero rates are respectively $4\mathrm{.}2\%,4\mathrm{.}8\%$ and $5\mathrm{.}6\%$ per annum. What is the $2Y$ zero rate assuming all rates are quoted with semiannual compounding?