Chicago Public Schools could spend about $50 million to entice its oldest, most expensive teachers to retire at the end of next year, the Chicago Sun-Times has found.

That’s if — and it’s still a big if — at least 1,500 teachers agree to accept a one-time bonus of $1,500 per year of service for an average 22 years on the job, as they’ve been offered in the agreement that barely fended off a strike by the Chicago Teachers Union. And that’s about three times the number of teachers who retired at the end of the last tumultuous school year, according to their pension fund.

Similarly, classroom aides can collect $750 per year if at least 600 of them who’ve worked for 10 years also decide to retire. That’s at least $4.5 million more.

The cash-strapped district, still depending on the state for $215 million of its current budget, says it’ll pay the bonuses for staffers retiring in June 2017 by December 2017.

That’s how the perks save money for the school system: The lump-sum payments of an average $33,000 per teacher come out of the 2017-18 budget, after the expensive teachers are gone.

Mayor Rahm Emanuel’s administration has not yet revealed any details of the cost of the deal cut late last Monday night, minutes before a midnight deadline for teachers to strike, as they did in 2012.

The Sun-Times meanwhile has learned from a source that that the four-year agreement may cost an estimated $8.9 billion — or about $2.2 billion per year. And the CTU’s attorney estimated that the teachers’ deal will cost at least $100 million more than a proposal floated in January that the CTU’s Big Bargaining Team nixed.

But that cost difference likely wouldn’t stem from the retirement incentive because it appeared in that proposal last winter, albeit with teeth, that forced those numbers of teachers and aides to retire — or let the Board of Education reopen the whole contract.

The tentative agreement still needs ratification by the CTU’s full membership of about 25,000. The union’s House of Delegates will meet Wednesday night to discuss specifics, set up the referendum for members and make a recommendation that isn’t binding.

Chicago Public Schools has been loath to discuss details of the full deal, saying it wanted to give teachers a chance to talk first.

But responding to Sun-Times analysis on Friday, district spokeswoman Emily Bittner said that the program aimed at removing teachers earning $85,000 to $100,000 from CPS’ payroll. Beginning teachers earn about $50,000 each, so the salary gap has “domino effects” for future raises and pension payments. The lump-sum payments don’t count toward pension benefits and are only for teachers already retirement eligible.

A source close to the negotiations said the savings in 2017-18 are nominal, but they jump the following year to between $80 million and $90 million.

With CPS enrollment dwindling, the district may not need to replace all of the retirees either, the source said.

Of course, if the minimum number of staffers don’t accept the bonus, CPS could spend nothing. CPS provided no predictions. The CTU didn’t respond to messages seeking comment.

Just 500 teachers retired last year, according to the Chicago Teachers Pension Fund, and a little more than 3,100 teachers are “retirement eligible,” meaning they have worked a certain number of years of service depending on their ages.

If the minimum of 1,500 teachers apply for $1,500 per year for 22 years — the average length of service identified by the pension fund — CPS would pay roughly $49.5 million. If all 3,100 want out of the classroom, that estimate could skyrocket.

Each teacher over 62 needs five years of service, a minimum $7,500 payout each. Those over 60 need at least 20 years of service, at least $30,000 each. Anyone under 60 but over 55 needs 33.95 years of service, at least $49,500 each.

As for the paraprofessionals, all that’s certain is that each of the 600 would cost CPS a minimum of $7,500. The Municipal Employees Annuity and Benefit Retirement Fund, which handles their pensions, said it could not provide any information without a Freedom of Information Act request.

Staffers would need to retire in June 2017. They must submit their notice by March 31, and if the minimum number of employees don’t take the deal, the sweetener goes away and the workers can rescind their intent to retire.