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 $6$M$,12$M$,$ and $18$M zero rates are respectively $4\mathrm{.}2\%,4\mathrm{.}8\%$ and $5\mathrm{.}6\%$

per annum. What is the $2$Y zero rate assuming all rates are quoted with

semiannual compounding?