Michael is single and $35$ years old. He is a participant in his employer's sponsored retirement plan. How much can Michael directly contribute to a Roth IRA in $2023$ in each of the following alternative situations?

a$.$ Michael's AGI before the IRA contribution deduction is $$50,000.$ Michael contributed $$3,000$ to a traditional IRA.

b$.$ Michael's AGI is $$160,000$ before any IRA contributions.