Consider a long forward $($i$.$e$.,$ long position means to buy$)$ a non dividend$-$paying stock in $3$ months. Assume the current stock price is $$40$ and the $3-$months risk$-$free interest rate is $5\%$ per annum. Given the following two arbitrage strategies, first, when the forward price is $$43$ and second, when the forward price is $$39$ determine the amount of money that is locked in by these two strategies.

$1.$ Forward price is $$43.$ An arbitrageur can borrow $$40$ at the risk free interest rate of $5\%$ per annum, buy one share, and short a forward contract to sell one share in $3$ months. At the end of the $3$ months, the arbitrageur delivers the share and receives $$43.$ Calculate the profit that is locked in$\mathrm{.}2.$ Forward price is $$39.$ An arbitrageur can short one share, invest the proceeds of the short sale at $5\%$ per annum for $3$ months and take a long position in a $3-$months forward contract. Calculate the net gain of this trading strategy$\mathrm{.}3.$ Under what circumstances do arbitrage opportunities not exist?