The premium of a call option with a strike price of $45 is equal to $5 and the premium of a call option with a strike price of $50 is equal to $3.5. The premium of a put option with a strike price of $45 is equal to $3. The risk-free rate of interest is 8%. In the absence of arbitrage opportunities, what should be the premium of a put option with a strike price of $50? All these options have a time to maturity of 3 months. ( not allowed to use the put-call parity to solve this problem)