Consider a European call option on a non$-$dividend paying stock. The current price of the stock underlying the option is $$45.$ The strike price of the option is $$41.$ The risk$-$free rate is $7\%$ per year. The volatility is $25\%$ per year. The option expires in $9$ months.

A$)$ Fill in the table for the variables needed to apply the Black$-$Scholes$-$Merton model.

B$)$ Calculate d$1$ and d$2.$ Be sure to use excel function to calculate the natural log$,$ square root, and exponential terms. Calculate N$($d$1)$ and N$($d$2)$ using the excel function $=$NORM.DIST$($d$,0,1,1).$ Calculate the price of the call option according to the Black$-$Scholes$-$Merton formula.

C$)$ Analyze the effect of a change in the stock price on the call price. Fill in the table. Create a plot of strike price $($x$-$axis$)$ vs$.$ call option price $($y$-$axis$).$

D$)$ Analyze the effect of a change in the risk$-$free rate on the call price. Fill in the table. Create a plot of risk$-$free rate $($x$-$axis$)$ vs$.$ call option price $($y$-$axis$).$

E$)$ Analyze the effect of a change in the volatility on the call price. Fill in the table. Create a plot of volatility $($x$-$axis$)$ vs$.$ call option price $($y$-$axis$).$

F$)$ Analyze the effect of a change in the time to expiration on the call price. Fill in the table. Create a plot of time to expiration $($x$-$axis$)$ vs$.$ call option price $($y$-$axis$).$ Please show work on excell