The owners of luxury second homes in New York City will have limited time and options to appeal the new pied-à-terre tax after receiving notice of their bills next month.

City officials are moving quickly to implement the tax on second homes to ensure it raises the $500 million it’s expected to generate this fiscal year, which ends June 30, 2027. New York Gov. Kathy Hochul (D) proposed the second-home tax in April to help fill a multibillion budget gap projected by the city this fiscal year, after spurning calls to raise income taxes on …