Consider a forward contract on a stock that matures in $6$ months. The spot price of the underlying stock is $$20.$ There are dividends of $$2$ expected from the ownership of this stock exactly in $6$ months from now.

Currently the forward price of this stock in the market is $$21.$ The annual risk$-$free rate of interest is $4\%.$

a$)$ Identify, whether there are any arbitrage opportunities available in these conditions.

b$)$ Identify a strategy that allows to earn riskless profits in the conditions described and calculate the riskless profits.