Given that the market price of the GOOG stock on $15$th March $2019$ is $$1,185\mathrm{.}55,$ calculate the European call price for a strike price of $$1,220$ using the two$-$step binomial pricing model.

$1($a$).$Use the yearly volatility of $0\mathrm{.}28\%$ and the risk$-$free rate of $1\%$ per annum. Also, you consider the number of days between $14$th March $2019$ and $20$th September $2019($expiration date$)$ to be $190,$ and the number of days in a year $365.$ Show the steps in detail.

$1($b$).$ Would this be an American option? If so$,$ what would be the American call price?

$1($c$).$ Explain why or why not the call price calculated using the binomial model is the same as what you see in the quotations.