A stock price has an expected return of $9\%$ and a volatility of $25\%.$ It is currently $$40.$ What is the price of a binary option that pays $$100$ if the stock price in $6$ month is higher than $$50?$ Assume the risk$-$free rate is zero.

a$.15\mathrm{.}44$

b$.86\mathrm{.}35$

c$.13\mathrm{.}65$

d$.8\mathrm{.}84$