European put and call options both have an exercise price of $$50$ that expires in $6$ months. The underlying asset is priced at $$52$ today and makes no dividend payments during the life of the option. The risk$-$free rate is $4\mathrm{.}5\%$ per annum continuous compounding and the put is selling for $$3\mathrm{.}80.$

$(1)$ According to the put$-$call parity, what is the price of the call option?

$(2)$ If the call option price is $$6\mathrm{.}00,$ is there an arbitrage opportunity? If your answer is yes, please brief describe the arbitrage strategy. please show work