The current price of a stock is $$16.$ In $6$ months, the price will be either $$20$ or $$12.$ The annual risk$-$free rate is $6\%.$ Find the price of a call option on the stock that has a strike price of $$13$ and that expires in $6$ months. $($Hint: Use daily compounding.$)$ Assume a $365-$day year. Do not round intermediate calculations. Round your answer to the nearest cent.