Problem $5$: Calculate net tax due

Saji and Henry Lozano are married for all of $2023$ and have an AGI of $$130,000,$ taxable income of $$120,000$ and calculated income tax liability of $$50,000.$ Their income tax liability in $2022$ was $$40,000($And $2022$ AGI was $$125,000),$ and they made the minimum amount of withholding and estimated income tax payments to ensure that they will not be subject to any estimated tax penalties. In addition, they had $$5,700$ withheld from their wages for their portion of Social Security and Medicare taxes and provided you with the following information:

They maintained a home for Saji's dependent $85$ year old father.

They have one child, Joshua, who is $15$ years old and meets the requirements of a qualifying child. During the year they spend $$10,000$ on a nanny to watch him while they are both at work $($you can assume they make equal amounts of earned income$).$

Required: What is the Lozano's net tax due$($refunded$)$ for $2023?$