The spot rates for $6,12,18,$ and $24$ months are $3\%,3\mathrm{.}25\%,3\mathrm{.}5\%,$ and

$3\mathrm{.}75\%,$ with semiannual compounding.

$($a$)$ Calculate the price of a two$-$year $4\%$ bond with semiannual payments.

$($b$)$ Calculate the yield to maturity of the bond in $($a$)$