PLEASE GIVE EXACT EXCEL STEPS.

Question $4$: Consider a European put option with an exercise price of $$102\mathrm{.}5$ and remaining time to maturity of $90$ days. The underlying asset of the option is a non$-$dividend$-$paying stock currently trading at $$102.$ This stock has a historical volatility of $40\%$ per year. Continuously compounded riskfree interest rate is $4\mathrm{.}5\%.$

A$.$ Find the price of the put option using the Black$-$Scholes option pricing model. Show all steps. $(10$ points$)$

B$.$ If the price of the underlying stock increases by $$0\mathrm{.}50,$ what would be the change in the price of the put option when only Delta is used to estimate change in price of an option? $(3$ points$)$

C$.$ If time to maturity changes by one day while all other variables remain the same in the Black$-$Scholes Option pricing model, what is the change to the price of the put option found in part $A?(7$ points$)$