Colleen is a cash basis, calendar year individual taxpayer who has a filing status of "single". Colleen's taxable income for $2023$ is $$195,000.$ Colleen's total tax prepayments for $2023$ are $$52,000.$ Colleen has no tax credits and owes no other taxes that are filed on the Form $1040.$ Using the tax table below:

SINGLE

$\backslash$table$[[$Taxable Income,Tax Rate in $2023],[$$$0-$$$11,000,10\%],[$$$11,001-$$$44,725,$$$1,100$ plus $12\%$ of the amount over $$11,000],[$$$44,725-$$$95,375,$$$5,147$ plus $22\%$ of the amount over $$44,725],[$$$95,376-$$$182,100,$$$16,290$ plus $24\%$ of the amount over $$95,375],[$$$182,101-$$$231,250,$$$37,104$ plus $32\%$ of the amount over $$182,100],[$$$231,251-$$$578,125,$$$52,832$ plus $35\%$ of the amount over $$231,250],[$$$578,126$ or more,$$174,238\mathrm{.}25$ plus $37\%$ of the amount over $$578,125]]$

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$($a$)$ Determine Colleen's "gross tax liability" for $2023?$

$($b$)$ Determine Colleen's $$additional tax due or net tax refund" for $2023?$

$($c$)$ What is Colleen's "marginal tax rate" for $2023?$

$($d$)$ What is Colleen's "effective tax rate" for $2023?$

$16.$ A$.$ Given the same facts as in #$15$ above and assuming that Colleen wants to minimize her total tax liability, would she prefer a $20\%$ refundable tax credit or a $100\%$ deduction for $($toward$)$ adjusted gross income for a $2023,$$$2,000$ annual expenditure for child care?

B$.$ Answer the question posed in #$16$ above but assume that Colleen's taxable income for $2023$ is $$24,000$ Would your answer be different?