Given the maturity of an American put option $2$ years, riskfree rate $10\%,$ volatility of the stock $40\%,$ current spot price of stock $$50,$ strike price $$50,$ what is the terminal payoff of the option when the stock price is $69\mathrm{.}312$ in a $3-$step binomial tree?

A$.$

$0$

B$.$

$13\mathrm{.}931$

C$.$

$10\mathrm{.}204$

D$.$

$31\mathrm{.}231$