Last year the Los Angeles City Council cut $150 million from the Police Department’s budget and promised to put that money into other social services.

Council members found much of the savings by slashing the funding available for LAPD overtime. But before they did, they received a warning: Many officers would end up working overtime anyway, and if there wasn’t enough money to pay them, those hours would wind up on the city’s so-called credit card.

Which is exactly what happened.

During the budget year that ended June 30, LAPD officers worked more than 680,000 overtime hours for which they have not yet been compensated, according to figures provided to The Times by the LAPD and the city’s financial analysts. Those hours, currently valued at $47.3 million, represent nearly a third of last year’s cut to the LAPD.

When those officers get paid, potentially years in the future, the cost will almost certainly be more expensive, said Dustin DeRollo, spokesman for the Los Angeles Police Protective League, the union that represents rank-and-file LAPD officers. That’s because that delayed overtime must be paid at an officer’s most recent salary, which is typically higher than when they worked the hours, because of pay increases or other factors.