In $2023,$ Amanda and Jaxon Stuart have a daughter who is $1$ year old. The Stuarts are full$-$time students and are both $23$ years old. Their only sources of income are gains from stock they held for three years before selling and wages from part$-$time jobs.

What is their earned income credit in the following alternative scenarios if they file jointly?

EXHIBIT $8-102023$ Earned Income Credit Table

Qualifying Children $(1)$

Maximum Earned Income Eligible for Credit $(2)$

Credit $\%(3)$

Maximum Credit

$(1)\backslash$times $(2)(4)$

Credit Phase$-$Out for AGI $($or earned income if greater$)$ over This Amount $(5)$

Phase$-$Out Percentage No Credit When AGI $($or earned income if greater$)$ Equals or Exceeds This Amount $(4)+[(3)/(5)]$

Married taxpayers filing joint returns

$0$ $ $7,8407\mathrm{.}65\%$ $ $600$ $$16,3707\mathrm{.}65\%$ $$24,210$

$111,750343,99528,12015\mathrm{.}9853,120$

$216,510406,60428,12021\mathrm{.}0659,478$

$3+16,510457,43028,12021\mathrm{.}0663,398$

All taxpayers except married taxpayers filing joint returns

$0$ $ $7,8407\mathrm{.}65\%$ $ $600$ $ $9,8007\mathrm{.}65\%$ $$17,640$

$111,750343,99521,56015\mathrm{.}9846,560$

$216,510406,60421,56021\mathrm{.}0652,918$

$3+16,510457,43021,56021\mathrm{.}06$ $$56,838$

c$.$ Their AGI is $$30,000,$ consisting of $$23,000$ of wages and $$7,000$ of lottery winnings $($unearned income$).$

Note: Round your intermediate calculations to the nearest whole dollar amount.

d$.$ Their AGI is $$30,000,$ consisting of $$5,000$ of wages and $$25,000$ of lottery winnings $($unearned income$).$

Note: Round your intermediate calculations to the nearest whole dollar amount.