Suppose you are given the following data for firm X$,$ assuming the option is at$-$the$-$money, and the stock price is $$45,$ the time to maturity is $60$ days, the stock variance is $0\mathrm{.}25$ per year and the risk$-$free rate $5\mathrm{.}5\%$ per year.

i$.$ Calculate the call and put option price using the Black$-$Scholes model.

ii$.$ What would be the new call price if the company pays a dividend yield of $6\%$ per year? Is the change in call price consistent with the effect you would observe when dividends are paid? Explain