Please solve the questions step by step with equations and answers.A stock price is currently $$200.$ It is known that at the end of $10$ months it will be either $$220$ or $$188.$ The risk$-$free interest rate is $7\%$ per annum with continuous

compounding. Consider a portfolio consisting of a long position in $$ shares of the stock and a short position in one put option to evaluate a $10-$month European

put option with a strike price of $$204.$

$(1)$ The portfolio is riskless when $$ is

$(2)$ The present value of the riskless portfolio is

$(3)$ The value of the put option is

$(4)$ The value of a $10-$month European call option with a strike price of $$204$ is