$$ In addition to the five factors, dividends also affect the price of an option.

The Black$-$Scholes Option Pricing Model with dividends is: C$=$S$\backslash$times e$$dt$\backslash$times N$($d$1)$E$\backslash$times e$$Rt$\backslash$times N$($d$2)$ d$1=[$ln$($S$/$E$)+($R$$d$+\backslash$sigma $2/2)\backslash$times t$](\backslash$sigma $\backslash$times t$)$ d$2=$d$1\backslash$sigma $\backslash$times t$$ All of the variables are the same as the Black$-$Scholes model without dividends except for the variable d$,$ which is the continuously compounded dividend yield on the stock.

A stock is currently priced at $$84$ per share, the standard deviation of its return is $60$ percent per year, and the risk$-$free rate is $5$ percent per year, compounded continuously. What is the price of a put option with a strike price of $$80$ and a maturity of six months if the stock has a dividend yield of $3$ percent per year?