$(8$ points$)$ Consider a European call option on a stock when there are ex$-$dividend dates in one months and four months. The dividend on one month is expected to be $$0\mathrm{.}5$ while the dividend on four months is expected to be $$10.$ The current share price is $$45,$ the exercise price is $$45,$ the stock price volatility is $25\%$ per annum, the risk$-$free rate of interest is $10\%$ per annum, and the time to maturity is six months. $($a$)$What is the value of call price? $(4$ points$)($b$)$ If the option is American rather than European $(4$ points$).$ Use Black's approximation to find the value of American call.