The price of a stock is currently $$50.$ It is known that at the end of six months it will be

either $$45$ or $$55.$ The risk$-$free interest rate is $10\%$ per annum with continuous compounding.

What is the value of a six$-$month European put option with a strike price of $$50?$ Please use

the one$-$period risk$-$neutral valuation to solve this problem. Assume continuous compounding.

You do not necessarily need to draw the tree.