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Ques. $5$ A stock price is currently $$50.$ It is known that at the end of six months it will be either $$60$ or $$42.$ The risk$-$free rate of interest with continuous compounding is $12\%$ per annum. Calculate the value of a two three$-$month European and American call option on the stock with an exercise price of $$48.$ Applying Binomial option pricing model to value the option, calculate the value of both options. $($Note: Value European and American is required to be calculated$).$