Consider an option on a non$-$dividend$-$paying stock when the stock price is $$30,$ the exercise price is $$29,$ the risk$-$free interest rate is $5\%$ per annum, the volatility is $25\%$ per annum, and the time to maturity is four months.

$($a$)$ What is the price of the option if it is a European call? $(9$ marks$)$

$($b$)$ What is the price of the option if it is an American call? $(2$ marks$)$

$($c$)$ What is the price of the option if it is a European put? $(4$ marks$)$

$($d$)$ Verify that put$-$call parity holds. $(5$ marks$)$