D$.$ Consider a stock whose current price is $$5,$ the stock price volatility is $30\%$ per annum, and the risk$-$free rate of interest is $6\%$ per annum. By considering the Black Scholes modelling dynamics,

$($i$)$ Calculate the price of an at$-$the$-$money call option on the stock expiring one year from today.

$[3$ marks$]$

$1($ii$)$ Calculate the price of the corresponding put on the same stock with the same strike price, expiring one year from today.

$[2$ marks$]$