Suppose the current value of a popular stock index is $649\mathrm{.}50$ and the dividend yield on the index is $2\mathrm{.}8\%.$ Also, the yield curve is flat at a continuously compounded rate of $5\mathrm{.}5\%.$

If you estimate the volatility factor for the index to be $18\%,$ use the Black$-$Scholes model to calculate the value of an index call option with an exercise price of $662$ and an expiration date in exactly three months. You may use Appendix D to answer the question. Do not round intermediate calculations. Round your answer to the nearest cent.

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If the actual market price of this option is $$21\mathrm{.}00,$ calculate the implied volatility coefficient. Do not round intermediate calculations. Round your answer to two decimal places.

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