$(25$ marks$).$ A $3-$year $6\%$ bond pays coupon semiannually. The term structure is

given as

Year $00\mathrm{.}511\mathrm{.}522\mathrm{.}53$

Interest Rate $22\mathrm{.}252\mathrm{.}52\mathrm{.}7533\mathrm{.}25$

All rates are semiannually compounded.

$($a$)$ Calculate the price of the bond.

$($b$)$ Calculate the duration of the bond.

$($c$)$ Calculate the bond$$s yield to maturity.

$($d$)$ If the bond$$s yield to maturity changes by $1\%,$ how much does the bond price

approximately change?