Use the Black$-$Scholes formula for the following stock:

Time to expiration $6$ months

Standard deviation $47\%$ per year

Exercise price $$59$

Stock price $$59$

Annual interest rate $4\%$

Dividend $0$

Recalculate the value of the call with the following changes:

a$.$ Time to expiration $3$ months

b$.$ Standard deviation $20\%$ per year

c$.$ Exercise price $$67$

d$.$ Stock price $$67$

e$.$ Interest rate $6\%$