Question $1(20$ points$)$: You hold an American call option with a $$30$ strike price on a stock that currently sells at $$35.$ The risk$-$free rate of interest is rf$.$ Compare the cash flows at expiration from $($i$)$ exercising the option now and putting the $$5$ proceeds in a bank account that pays the risk$-$free rate until the expiration date and $($ii$)$ holding onto the option until expiration, selling short the stock today, and placing $$35$ you receive into the same bank account.