Assume that a stock trading for $$30$ today will be worth either $$25$ or $$35$ in two years. A risk$-$free asset offers an annualized $3\%$ return $($continuously compounded over that time period.

$$What is the price today of a two$-$year put option on this stock with a strike price of $$40?$ The maximum error is $0\mathrm{.}1.$