A stock trades for $43 per share. A call option on that stock has a strike price of $54 and an expiration date three months in the future. When the volatility of the stock's returns is 30%, the Black and Scholes value of the option is $3.82. Now assume, the volatility of the stock's returns is 55%, and the risk-free rate is 3%. By how much does the call price change? The Black and Scholes value of this call option is?

A previous chegg post of mine had an incorrect answer of $6.62 for the Black and Scholes value, below is the explanation and formulas needed to be used.

Try again. To calculate the value of the call option, use the Black and Scholes option-pricing model formulas below: Call price =( Stock price )( Probability 1)( Present value of strike price )( Probability 2), where Probability 1= Normsdist ( Value 1); Probability 2 = Normsdist ( Value 2); Value 1=(Standarddeviation)TimetoexpirationNaturallogof(StrikepriceStockprice)+(Risk-freerate+2(Standarddeviation)2)(Timetoexpiration); Value 2= Value 1( Standard deviation )Timetoexpiration