Hope is a self$-$employed taxpayer who turns $54$ years old at the end of the year $(2023).$ In $2023,$ her net Schedule C income was $$130,000.$ This was her only source of income. This year, Hope is considering setting up a retirement plan.

What is the maximum amount Hope may contribute to the self$-$employed plan in each of the following situations?

She sets up an individual $401($k$).$