Past exam of the martingales and financial mathematics course of the University of Oxford / 2010 / B / 4 / d

Use $q=1/2$ and discount one step by $R=1.1$. At the up node, $A_1=110$ and immediate exercise pays $5$. Continuation is worth $(0+5/3)/(2R)=25/33<5$. At the down node, $A_1=100$ and immediate exercise pays $15$, while continuation is $(25/3+15)/(2R)=350/33<15$. Thus the American put option should be exercised at either time-one node, and