For a stock, you are given:

$($i$)$ The stock's price is $40.$

$($ii$)$ The stock pays no dividends.

$($iii$)$ A $6-$month $30-$strike European put option has premium $3.$

$($iv$)$ A $6-$month $40-$strike Furopean put option has premium $6.$

$($v$)$ A $6-$month $45-$strike European call option has premium $3\mathrm{.}5.$

$($vi$)$ The continuously compounded risk$-$free interest rate is $0\mathrm{.}05.$

To exploit the mispricing, you sell three $40-$strike put options, buy one $30-$strike put option, and buy two synthetic $45-$strike put options created using appropriate amounts of $45-$strike call options, shares of stock, and risk$-$free bonds.

Calculate your net gain after $6$ months, including interest, if the stock price is $43$ then.