A binary $($or digital or cash$-$or$-$nothing$)$ put option pays $$100$ if the stock price is less than the strike K on date T$,$ and nothing otherwise. Consider a one$-$period binomial model with U $=1\mathrm{.}16,$ D $=1/$U$.$ The interest rate r satisfies $=1\mathrm{.}04,$ and suppose K is equal to the current stock price. What is the no arbitrage price of the digital put option at time zero? $[$round to two decimal places$]$

The correct answer is $38\mathrm{.}7286,$ please explain how this is achieved?