Part $3$: Problems $(1$ bonus point$)$

Eallstock Inc.$\text{'}$s stock price $S$ is $$45.$ European options on Eallstock have a strike price $K=$$$50,$ a

maturity $T=0\mathrm{.}5,$ the risk$-$free rate $r=5\%$ p$.$a$.,$ and let the volatility $=0\mathrm{.}25$ per year. The company

is going to pay a dividend of $50$ cents after in $4$ months.

a$.$ Compute the price of a call option using the Black$-$Scholes model.

b$.$ Compute the price of a put option.