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$1.$ A four$-$month European call option on a dividend$-$paying stock is currently selling for $$5.$ The stock price is $$64,$ the strike price is $$60$ and a dividend of $$0\mathrm{.}80$ is expected in one month. The risk$-$free interest rate is $12\%$ per annum for all maturities. What opportunities are there for an arbitrageur?

$2.$ The price of a European call that expires in six months and has a strike price of $$30$ is $$2.$ The underlying stock price is $$29$ and a dividend of $$0\mathrm{.}50$ is expected in two months and again in five months. The term structure is flat, with all risk$-$free interest rates being $10\%.$ What is the price of a European put option that expires in six months and has a strike price of $$30?$