how to solve this problem Question $4($Total $18$ marks$)$

The following table gives the relevant information of four bonds.

$\backslash$table$[[$Bond #$,$Time to Maturity $($years$),$Semiannual Coupon $($$$),$Bond Price $(\%$ of par$)],[1,0\mathrm{.}5,0\mathrm{.}0,97],[2,1\mathrm{.}0,0\mathrm{.}0,95],[3,1\mathrm{.}5,8\mathrm{.}0,99],[4,2\mathrm{.}0,10\mathrm{.}0,98]]$

a$)$ Calculate the zero rates for maturities of $6$ months, $12$ months, $18$ months, and $24$ months.

b$)$ What are the forward rates for the $6-$month periods: months $7$ to $12,$ months $13$ to $18,$ months $19$ to $24?$

c$)$ Estimate the price and the yield of a two$-$year bond providing a semiannual coupon of $7\%$ per annum. $($You may use the trial$-$and$-$error method to find the bond yield.$)$