Suppose todays stock price of book.com is $100. With probability of 60% the price will rise to $130 in one year and with probability of 40% it will fall to $80 in one year. A European put option with a strike price of $90 and a time to expiration of one year sells at $4.

a) What is the one year risk free rate implied by no-arbitrage?

b) What would be the no-arbitrage risk free rate be with a probability of 50% when the price increases and a probability of 50% if it decreases, keeping all other values constant