Problem $3\mathrm{.}5$

Under the same setup as in Problem $3\mathrm{.}4,$ compute the prices of :

$($a$)$ a $6-$month American call option with strike price $$101$

$($b$)$ a $6-$month American put option with strike price $$101.$

$($c$)$ Compare the prices of the American and European call options and comment on the result.