A stock is selling today for $$80.$ The stock has an annual volatility of $30$ percent, and the annual nominal risk$-$free interest rate is $3\mathrm{.}50$ percent.

a$.$ Calculate the fair price for a $16$ month European call option with an exercise price of $$84.$

b$.$ Calculate how much the current stock price would need to change for the purchaser of the call option to break even in $16$ months.

c$.$ Calculate the level of volatility that would make the $$84$ call option sell for $$18.($Use Goal Seek or Solver$).$