Problem 4. (20 points) Suppose that we have a stock with a price of $60 today and that in one year, the price will be either $90 or $30. The risk-free rate is 10% (simple annualized rate). Consider the payoffs to a call option with a strike price of $60. What is the value of the call option? (Hint: Construct a portfolio with the stock and the risk-free bond to replicate the payoff structure of the Call option. The value of the call option today must be equivalent to the value of the replicating portfolio to prevent arbitrage.)