Suppose that a stock is currently trading at $$50$ per share, and the risk$-$free interest rate is $2\%$ per annum. An investor purchases a call option with a strike price of $$55$ for a premium of $$2$ per share and sells a put option with the same strike price for a premium of $$4$ per share. Both options have an expiration date of $6$ months from now. The put option is European, meaning it can only be exercised on the expiration date, while the call option is American, meaning it can be exercised at any time before the expiration date.

What is the arbitrage$-$free price of the stock?