Using a binomial tree, when calculating the price of a $$40$ strike $6-$month European put option, using $3-$month intervals as the time period, what is the stock price at maturity $($at the end of period $2)$ if the stock price goes up and then down $($or down and then up$)?$ Assume the following data: S $=$ $$39\mathrm{.}70,\backslash$delta $=0\%,$ r $=5\mathrm{.}0\%,\backslash$sigma $=0\mathrm{.}35.$

Question $26$ options:

$$38\mathrm{.}8594$

$$37\mathrm{.}7316$

$$36\mathrm{.}8088$

$$40\mathrm{.}7050$

$$27\mathrm{.}3838$