Parents in New York City rolled their eyes at a recent survey that claimed it costs $15,447 a year to raise a child in the state, calculated over the course of 18 years. But families across the five boroughs told The Post that their annual bills far eclipse that, ranging from $19,000 to a shocking $100,000 per child.  The LendingTree study , published April 6, found that parents pay more than $300,000 to raise a child in the US over the course of 18 years. New York State was ranked at No.15 in