Suppose that you enter into a six$-$month forward contract on a stock when the stock price is $$30.$ A $$5$ dividend will be paid after $3$ months. The three$-$month and six$-$month risk$-$free interest rate $($with continuous compounding$)$ are $2\%$ and $4\%$ per annum. The actual forward price is $$40.$

$(1)$ The correct forward price is $

$.$

$(2)$ To arbitrage, you could

$($long$/$short$)$ a six$-$month forward contract on $1$ share of the stock.

$(3)$ The arbitrage profit per share is $

$$