You wish to create a synthetic $182-$day Treasury bill with maturity value $10,000.$ You are g

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

$($ii$)$ The stock pays continuous dividends proportional to its price at a rate of $2\%.$

$($iii$)$ A $182-$day European put option on the stock with strike price $K$ costs $0\mathrm{.}80.$

$($iv$)$ A $182-$day European call option on the stock with strike price K costs $5\mathrm{.}20.$

$($v$)$ The continuously compounded risk$-$free interest rate is $5\%.$

Determine the number of shares of the stock you should purchase.