Suppose that the price of stock is $$100.$ After $6$ months, the price can go up to $$120$ with probability $\frac{1}{2}$ and down to $$90$

with probability $\frac{1}{2}.$ Assume the $6-$month effective interest rate is $5\%.$ Consider a put option with strike price $$100$ and

expiration $0\mathrm{.}5$ year. What is a fair price of the option?