Harrington Company is giving each of its employees a holiday bonus of $$250$ on December $13,20-($a nonpayday$).$ The company wants each employee's check to be $$250.$ The supplemental tax percent is used.

Nobody has capped for OASDI prior to the bonus check.

You may need to add one penny to the gross so that net bonus is exactly $$100\mathrm{.}00.$ Round your calculations and final answers to the nearest cent.

As we go to press, the federal income tax rates for $2024$ are being determined by budget talks in Washington, and are not available for publication. For this edition, the $2023$ federal income tax tables for Manual Systems with Forms W$-4$ From $2020$ or Later with Standard Withholding and $2023$ FICA rates have been used.

a$.$ What will be the gross amount of each bonus if each employee pays a state income tax of $3\mathrm{.}01\%($in addition to the other payroll taxes$)?$ Round your calculations and final answers to the nearest cent.

b$.$ What would the net amount of each bonus check be if the company did not gross$-$up the bonus? Round your intermediary calculations to the nearest cent.