In $2024,$ Nadia is single and has $$106,000$ of regular taxable income. She itemizes her deductions as follows: real property taxes of $$1,800,$ state income taxes of $$2,300,$ and mortgage interest expense of $$11,500($acquisition indebtedness of $$200,000).$ In addition, she receives tax$-$exempt interest of $$1,600$ from a municipal bond $($issued in $2006)$ that was used to fund a new business building for a $($formerly$)$ out$-$of$-$state employer. Finally, she received a state tax refund of $$450$ from the prior year.

Note: Amounts to be deducted should be indicated by a minus sign.

a$-1.$ What is Nadia's AMTI this year if she deducted $$15,750$ of itemized deductions last year $($including a total of $$4,150$ of real property taxes and state income taxes$)$ and did not owe any AMT last year?