The price of a European call and put on a stock are $$2$ and $$5,$ respectively. Both have a strike price of $$45$ and an expiration date of $6$ months. The current stock price is $$40$ and the continuously compounded dividend yield is $3\%.$ Markets are assumed to be free of arbitrage.

a$)$ What is the market implied $6-$month risk$-$free interest rate?

b$)$ What is the market implied $6-$month forward price on a forward contract on the stock?

c$)$ What is the market implied $6-$month cost of carry?