$11\mathrm{.}29.$ Consider a put option on a non$-$dividend$-$paying stock when the stock price is $$40,$ the strike price is $$42,$ the risk$-$free interest rate is $2\%,$ the volatility is $25\%$ per annum, and the time to maturity is three months. Use DerivaGem to determine the following:

$($a$)$ The price of the option if it is European $($use Black$$Scholes: European$)$

$($b$)$ The price of the option if it is American $($use Binomial: American with $100$ tree steps$)$

$($c$)$ Point B in Figure $11\mathrm{.}7.$Figure $11\mathrm{.}7$ Variation of price of a European put option with the stock price.