Roger Rogers, $46,$ works for the local public school teaching Physics to advanced science high school students. Roger has been with the school for $21$ years, earns $$65,000$ per year, and has never contributed to the $403($b$)$ retirement plan that is offered. The $403($b$)$ plan offers dollar for dollar matching on all contributions. The school district is considering adoptiong a $457$ plan.

What amount would Roger be able to defer from taxes in $2022$ with the $403($b$)$ plan?

a$.$ $$3,000.$

b$.$ $$20,500.$

c$.$ $$23,500.$

d$.$ $$68,000.$