$($a$)$ What does it mean if a coupon bond is trading at par? $(2$ marks$)$

$($b$)$ An investor paid $\backslash (95\backslash )$ for a zero$-$coupon bond with face value $\backslash (100\backslash )$ maturing in six months. When will the bond value reach $\backslash (99\backslash )$ if the interest rate remains the same? $(5$ marks$)$

$($c$)$ A coupon bond with face value $\backslash (100\backslash )$ and coupons of $\backslash (4\mathrm{.}50\backslash )$ paid annually has maturity in three years. The current annual interest rate is $\backslash (4\mathrm{.}19\backslash \%\backslash ).$ The expected interest rate in the following two years is $\backslash (3\mathrm{.}75\backslash \%\backslash )$ and $\backslash (3\mathrm{.}50\backslash \%\backslash ),$ respectively. The investment of $\backslash (3450\backslash )$ is invested into the coupon bond, and all coupons are reinvested into the same type of bonds at the beginning of each year.

$($i$)$ Find the price of the coupon bond at the beginning of each year. $(6$ marks$)$

$($ii$)$ Find the number of bonds held during the first, the second and the third year. $(6$ marks$)$

$($iii$)$ Find the value of the investment after $3$ years. $(2$ marks$)($iv$)$ Estimate the coupon bond yield expressed per annum. $(4$ marks$)$