Consider a two period binomial tree with S₀ = $12, u = 1.10, d = 0.90, r = 0.06 (annual continuously compounded). Suppose you have a non-dividend paying stock and an American put option on the stock with strike price $12.50 maturing in one year.

Find the price of an American put option at time zero, using risk-neutral pricing. Find the number of shares of the stock (Delta) and the amount of risk-free bonds (B) at each node.