Mattola Company is giving each of its employees a holiday bonus of $$100$ on December $13,20--($a nonpayday$).$ The company wants each employee's check to be $$100.$ The supplemental tax percent is used.

Nobody has capped for OASDI prior to the bonus check.

As we go to press, the federal income tax rates for $2023$ are being determined by budget talks in Washington, and are not available for publication. For this edition, the $2022$ federal income tax tables for Manual Systems with Forms W$-4$ from $2020$ or Later with Standard Withholding and $2022$ FICA rates have been used.

a$.$ What will be the gross amount of each bonus if each employee pays a state income tax of $2\mathrm{.}8\%($in addition to the other payroll taxes$)?$

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.

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.