A stock price is currently 50. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% with continuous compounding.

a) What is the value of a six-month European put option with a strike price of 51?

b) If the corresponding put option were American, would it ever be optimal to exercise it early at any of the nodes on the binomial tree?