The current price of a stock is $$94,$ and a three$-$month call options with a strike price of $$95$ currently sell for $$4\mathrm{.}70.$ An investor who feels that the price of the stock will increase is trying to decide between buying shares of the stock and buying call options. Both strategies involve an investment of $$9,400.$ The continuously compounded risk$-$free rate is $6\%$ per annum.

a$)$ How high does the stock price have to rise for the option strategy to be more profitable?

b$)$ What is the lower bound on the call option price?

c$)$ Does the current market price for the call option offer any arbitrage opportunities?

d$)$ What should be the fair price of a put option with the same underlying stock, strike price and maturity?