Consider a Black$-$Scholes model, where the risk$-$free rate is $r=0\mathrm{.}03,$ the volatility is $=0\mathrm{.}1,$ and

$S(0)=$$$350$

i$)$ Find the price of a European call with strike price $K=$$$300$ and expiration $T=1.$

ii$)$ Compute the Greeks $($Delta$,$ Gamma, Theta, Rho, Vega$),$ for $t=0\mathrm{.}5$ and $S(0\mathrm{.}5)=$$$400,$ for the

European call of i$).$

iii$)$ Find the price of a European put with strike price $K=$$$320$ and expiration $T=1.$

iv$)$ Compute the Greeks $($Delta$,$ Gamma, Theta, Rho, Vega$),$ for $t=0\mathrm{.}5$ and $S(0\mathrm{.}5)=$$$400,$ for the

European put of iii$).$