The price of a stock is currently $$40.$ It is known that at the end of three month it will be either $$44$ or $$32.$ The risk$-$free interest rate of return is $4\%.$ Assume continuous compounding and there is no arbitrage opportunity in the economy. Please use the one$-$period risk$-$neutral valuation to solve the following questions.

$($a$)(8$ points$)$ What is the value of a three$-$month European call option with a strike price of $$42,$ in an arbitrage$-$free economy?

$($b$)(8$ points$)$ What is the value of a three$-$month European put option with a strike price of $$36,$ in an arbitrage$-$free economy?