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? $($b$)$ What is the price of the option if it is an American call? $($c$)$ What is the price of the option if it is a European put? $($d$)$ Verify that put$$call parity holds.Consider an option on a non$-$dividend$-$paying stock when the stock price is $$30,$ the exercise price is $$29,$ the risk$-$free interest rate is $5\%$ per annum, the volatility is $25\%$ per annum, and the time to maturity is four months. $($a$)$ What is the price of the option if it is a European call? $($b$)$ What is the price of the option if it is an American call? $($c$)$ What is the price of the option if it is a European put? $($d$)$ Verify that put$$call parity holds.