Use the Black$-$Scholes option pricing model to price the following European put option on a stock. The stock is currently trading at $$81\mathrm{.}50,$ with a dividend yield of $3\%$ per year. The exercise price of the option is $$80,$ and the option has $6$ months to expire. The volatility of the stock return is $19\%,$ and the risk$-$free rate is $5\mathrm{.}5\%.$

a$.$ Compute d$1.$ Use the normal probability distribution table to look up the value for $N(d1).$

b$.$ Compute d$2.$ Use the normal probability distribution table to look up the value for N$($d$2).$

c$.$ What is the value of this put option?