The current price of a non$-$dividend$-$paying stock is $$68\mathrm{.}73$ and you expect the stock price to either go up by a factor of $1\mathrm{.}324$ or down by a factor of $0\mathrm{.}799$ each period for $2$ periods over the next $0\mathrm{.}8$ years. Each period is $0\mathrm{.}4$ years long.

A European put option on the stock expires in $0\mathrm{.}8$ years. Its strike price is $$69.$ The risk$-$free rate is $7\%($annual$,$ continuously compounded$).$