Normandy Company granted $5,000$ stock options to key executives when the stock price was $$12$ per share. The options vest in $4$ years, are exercisable at $$12$ per share for $3$ years after vesting, and have a fair value of $$5$ per option. As of the end of the first year, Normandy believed that all the options would vest, and recorded compensation expense of $$6,250.$ In the second year, Normandy revised its expected forfeiture rate to $10\%.$ What will be the amount of compensation expense Normandy will record for the options in year $2?$

$$6,250$

$$5,625$

$$5,000$

$$5,417$