Suppose that the $3-$year and $3\mathrm{.}5-$year zero rates with continuous compounding are $2\mathrm{.}5\%$ and $2\mathrm{.}55\%,$ respectively.

$($a$)$ What is the forward rate for the six$-$month period beginning in $3$ years $(3$R$35)($from Year $3$ to Year $3\mathrm{.}5)$ with continuous compounding?

$($b$)$ What is the forward rate for the six$-$month period beginning in $3$ years $(3$R$3\mathrm{.}5)($from Year $3$ to Year $3\mathrm{.}5)$ with semiannual compounding?

$($c$)$ What is the $($Year $0)$ value of an FRA that promises to pay the lender $2\mathrm{.}75\%($compounded semiannually$)$ on a principal of $$3$ million for the six$-$month period starting in $3$ years $($from Year $3)$