A cash or nothing option pays a fixed amount of $$70.$ If the asset finishes above the strike price of $$100$ at the end of a six months the stock price is $$100.$ And the Volatility of the stock is $20\%$

assume that N$($d$1)$ and N$($d$2)$ from the BSM model are $0\mathrm{.}9151$ and $0\mathrm{.}9602$ respectively

$1.$ Is it a call or a put? why?

$2.$ Given a risk rate of $3\%$ calculate the price of this cash or nothing option.

$3.$ What is the profit of the stock price at maturity is $$120$