Lithium mining is becoming more popular because of the demand for batteries in electric vehicles. Assume that you have the rights to a lithium mine and the most recent valuation of the mine was $7\mathrm{.}2$ million. Changes in the price of similar mines have an annual standard deviation of $20\%.$ A buyer has recently approached you and wants an option to buy the mine in the next $12$ months for $7\mathrm{.}5$ million. The risk$-$ free rate of interest is $3\%$ per year, compounded continuously. How much should you charge for the option? Show all your workings.