The city is getting ready to cut its first checks to charter schools that are paying for their own space—an outlay that could stretch to nearly $10 million for this school year, based on charter school enrollment figures.

By the end of May, the Department of Education will have sent money to dozens of expanding charter schools to cover this year’s facility costs, according to a letter sent to school leaders this month. The schools are the first to reap the significant financial benefits of a state law passed just over a year ago that is sure to grow more costly for the city in the coming years.

“It’s huge,” said Great Oaks Charter School founder Michael Duffy, who became the first school leader to test the nascent law’s limits this summer. Duffy estimates his Lower Manhattan school stands to receive about $300,000 to cover rent for about 109 students in seventh grade this year.

Great Oaks is one of 46 city charter schools in private space that added grades, according to the New York City Charter School Center, and more than 3,600 students from those schools were enrolled in new grades. Most of those schools successfully appealed to the State Education Department for rental assistance over the last several months.

Under the law, eligible schools can receive up to 20 percent of their total school funding for those students — which this year rounds to $2,755 per student. (The actual amount paid to each school could be less, depending on how much the school pays in rent. The department is reviewing leases to calculate what to pay each school.)

Not all eligible schools have applied for the funding, a department spokesman said, though the charter center said most are expected to have applied or to apply in the future. If they do, the city would be on the hook for as much as $10 million for this school year, although that sum will likely be lower because some school leaders said they paid less than $2,755 per student in rent.

The spokesman said that a precise tally of costs would not be available until city reviews all of the appeals.

But the city’s costs are certain to continue to add up, as more schools open and enrollment increases at expanding schools. Next school year, the charter center’s enrollment projections would put the maximum tab just for expanding schools at $17.8 million.

One of those new schools, South Bronx Early College Academy Charter School, will be due more than $300,000 for 110 six graders next year, according to the founding principal.

“It’s a heck of a gift,” said the founder, Ric Campbell.

The city is obligated to spend $40 million to cover rent costs of eligible charter schools if they are not given space inside of a city-owned building, according to the law. Once the bills hit the $40 million ceiling, costs will be split with the state.

The law was passed in April 2014 as a rebuke to Mayor Bill de Blasio, who during his early months in office signaled that he would end the city’s practice of giving charter schools space inside of city-owned buildings for free. Charter schools do not automatically receive any funding for space, and de Blasio’s predecessor Michael Bloomberg used the controversial space-sharing policy to help grow the city’s charter sector.

“The challenge since the dawn of the charter school sector in New York City has been facilities,” said Duffy, who headed the education department’s charter school office from 2007 to 2010. The new facilities funding law, he added, “is the next chapter.”

Many of the schools set to receive the funding didn’t expect the financial boost when the law was passed last April. Lawmakers and members of Gov. Andrew Cuomo’s own staff indicated then that only brand-new schools would be covered.

But a conference call last May between charter school leaders and New York City Charter School CEO James Merriman kicked off what would become a broader campaign. Merriman, a lawyer, said his reading of the law suggested that existing schools could also take advantage of the funding as long as they were adding grades.

Duffy was the first leader of an existing school to request space from the city and, once denied, appealed to then-State Education Commissioner John King. On his last day in office, King upheld Great Oaks’ appeal, a decision that opened the floodgates for other schools to submit their own requests.

Not all the private rent bills will cost as much as the $300,000 that Duffy is expecting for Great Oaks, which next year will move into a school building that will be vacant after the charter school there now closes at the end of the school year.

For instance, there are just 13 students in 11th grade this year at John W. Lavelle Preparatory, according to President Ken Byalin. The most the school could receive for this year is about $36,000, but Byalin said it would be lower because its costs to operate inside corporate offices come out to less than $2,755 per student.

Byalin said that since the school’s rent is already paid for the year, the money might go toward providing summer school classes, more Saturday school days, or maybe to fund a trip for the school’s inaugural senior class next year.

Not all charter schools in private space are eligible for city money. Twenty-three are done adding grades, and are therefore ineligible, a funding discrepancy that has prompted a lawsuit from charter school parents and advocates.

And not all of the expanding schools in private space will receive it. New Dawn Charter High School in Brooklyn is a transfer school for students who had previously left other high schools and are behind in their academic credits. But because students enter the school at different ages and different levels of high school completion, the school doesn’t technically have any grades. So even though it is adding students, it is not technically “adding grades,” which disqualified the school, according to its principal.

“We argued that the wording in the law was not meant to be a barrier to a new school like us,” New Dawn principal Sara Asmussen said of her school’s rejected appeal. “But it’s fine. The law’s the law. That’s what it says.”