$5)$ Use the risk neutral probabilities to calculate the value of a three$-$month American put with the strike price $50$ as in problem $3.$ Calculate the put value at each node of the tree by comparing with early exercise value. Are there any nodes where you should early exercise the put?

Problem $3$ is this: $3)$ A stock price is $$50$ now. In $1$ month it can go $5\%$ up or down. In the second month it can go $5\%$ up or down. And in the third month it can go $5\%$ up or down. Construct a binomial tree for this stock. The annual interest rate is $10\%$ with continuous compounding.