Assume the Black$-$Scholes framework.

For a six$-$month at$-$the$-$money European put option on a stock, you are given:

$$ The current stock price is $$50.$

$$ The only dividend during the next $6$ months is $$2\mathrm{.}50$ to be paid in $4$ months.

$$ The continuously compounded risk$-$free interest rate is $6\%.$

Consider that sigma$=\mathrm{.}3$ and calculate the price of the put option.

Please do by hand and not through excel.