The S&P $500$ index is trading at a level of $1200.$ The rate of interest is $2\%.$ The average rate of dividends for stocks in the index is $3\%.$ Index volatility is $20\%.$ What is the Black$-$Scholes price of a one$-$year at$-$the$-$money put option on the index $($i$.$e$.$ strike $=1200)?$

$$87\mathrm{.}49$

$$88\mathrm{.}90$

$$89\mathrm{.}53$

$$90\mathrm{.}15$