Both a call and put currently are traded on stock $xYZ$; both have strike prices of $$50$ and maturities of six months.

a$.$ What will be the profit to an investor who buys the call for $$4$ in the following scenarios for stock prices in six months? $($i$)$ $$40$; $($ii$)$ $$45$; $($iii$)$ $$50$; $($iv$)$ $$55$; $($v$)$ $$60.$

b$.$ What will be the profit in each scenario to an investor who buys the put for $$6?$