Call options with an exercise price of $$50$ and one year to expiration are available. The market price of the underlying stock is currently $$42,$ but this market price is expected to either decrease to $$52$ or increase to $$37$ in a year's time. Assume the risk$-$free rate is $6\%.$ What is the value of the option? $($Do not round intermediate calculations. Round the final answer to $2$ decimal places. Omit any commas and the $ sign in your response. For example, an answer of $$1,000\mathrm{.}50$ should be entered as $1000\mathrm{.}50.)$

Numeric Response