please show all formulas and reasoning for this question, thank you in advance T

Question

please show all formulas and reasoning for this question, thank you in advance

The price of HighTech (HT) stock is $534.25. Your broker tells you that you could buy a European call option on HT with a strike price of $750 and 325 days until maturity for $54. Your research indicates that the standard deviation of HT’s stock returns is 55% and you know that the continuously compounded risk free rate is 5%. Would you be willing to buy such an option for the price quoted by your broker (i.e., $54)? Assume one year has 365 days and HighTech doesn’t pay any dividends. (Dividends complicate option pricing.)

Note: Round d1 and d2 to the nearest values in the cumulative normal distribution table. The table is posted on uLearn.

Explanation / Answer

please show all formulas and reasoning for this question, thank you in advance T

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