The following table gives the prices of bonds

Bond Principal $($$$)$ Time to maturity $($years$)$ Annual coupon $($$$)$ Bond Price $($$$)$

$1000\mathrm{.}5098$

$10015100$

$1001\mathrm{.}56100$

$10027101$

The bonds provide coupon are semiannual coupon bond

a$.$ Calculate $6-$month, $12-$month, $18-$month and $24-$month zero rates.

b$.$ What is the forward rate for the six$-$month period beginning in $12$ months.

c$.$ Estimate the price of a two$-$year bond providing annual coupon of $7\%$ annually.