Rutter Inc. granted $100,000$ stock options to executives and employees on January $1,2020.$ The options have a strike price is $$10$ per share and expire in $2025.$ The par value of the common stock is $$1.$ Using an option pricing model, the company calculates a fair value of $$30$ per share. The expected service period, or benefit period, is $3$ years.

a$.$ Prepare the journal entries for $2020$ and $2021.$

b$.$ In $2025,40\%$ of the options are exercised and the remaining options expire. Prepare the journal entries to record the exercise and expiration of the options.