SAN JOSE — When city leaders last year persuaded voters to approve new taxes, they said the money would pay for more police, faster emergency response, smoother roads and other improvements to services slashed during the last economic downturn.

But a chunk of the $52 million a year in new sales and business tax revenue voters approved last year will be consumed by a hefty spike in the city’s retirement costs — spurring some elected leaders to wonder if taxpayers are getting what they were promised.

“I feel it’s very unfair to taxpayers,” said Councilman Johnny Khamis, who opposed putting the sales tax hike on the ballot and preferred a measure dedicating the money to police and roads, which would have required a greater margin for approval. “We can make a claim that the money will go to street pavements and improving services, when in fact, most of it is going to pensions. It reduces the accountability and trust in government.”

Mayor Sam Liccardo, who supported last year’s tax measures, acknowledged that some of the new money will pay for the spike in retirement costs — but said city voters are still getting what they were promised.

San Jose is on the hook for the higher pension costs regardless of whether voters approved the tax measures, Liccardo noted. But the extra revenue ensures nothing else gets cut, he said, adding that San Jose is using some of the sales tax revenue to re-open fire stations and increase the number of community service officers. A spending plan pegged $3.9 million for hiring community service officers and maintaining minimum staffing levels at the fire department.

“With the benefit of better revenues as well as the measures’ passage, we are able to avoid a cut in services to pay the bill we are legally required to pay,” the mayor said.

Last June, San Jose voters approved Measure B, a quarter-cent sales tax for 15 years expected to generate about $40 million a year. In pitching it to voters, the city said it would pay for “improving police response to reduce violent crimes and burglaries,” speeding emergency response times, “repairing potholes and streets” and “expanding gang prevention.”

City voters in November approved Measure G, which increased tax revenue from businesses by an estimated $12 million a year. The city said it would “fund essential services such as police, emergency response, and pothole repair.”

Both were general tax measures that required only majority approval and whose revenues go into the city’s general fund to be spent as a majority of elected leaders see fit.

But since those measures passed, officials who oversee the city’s retirement plans delivered some bad news: the city’s projected pension and retiree healthcare costs will rise sharply, by $28.8 million more than previously projected in 2018, and up by $57 million by 2021, according to city reports.

Because most city workers are paid out of the city’s general fund, most of those higher retirement costs will come from the same pot as the new tax revenues, effectively offsetting them.

“Funding pensions is like funding the department of the past,” said Pete Constant, a former city councilman and the vice president of the Silicon Valley Taxpayers’ Association. “The majority of the pension increases we’re seeing are not paying for benefits of current officers — you’re paying debt from the past and you’re not getting anything for it.”

The retirement bill spiked primarily because the independent boards that oversee San Jose’s two retirement plans adopted less rosy assumptions about the benefits’ cost: They now assume employees and retirees will live longer, and that annual returns on pension fund investments will average 6.875 percent rather than 7 percent.

Pension reform advocates have long pushed for such steps. Overly optimistic assumptions that mask the real costs of benefits can leave pension systems badly underfunded, as most California public pension funds currently are, and force significant tax hikes and service cuts to cover obligations to retirees. In the worst cases, cities can wind up in bankruptcy and retirees can see their benefits cut.

But prudent steps to ensure pension plans are properly funded means higher costs to cities and their workers.

“If we expect to make less money in the future, that money has to come from somewhere,” said Roberto Peña, San Jose’s director of retirement services. “So the city and employees must contribute more.”

San Jose in 2012 famously tried to slash its rising retirement bill — which had more than tripled over a decade — with a ballot measure that called for reducing benefits for current workers, future hires and retirees. Nearly 70 percent of city voters approved that Measure B, which Liccardo supported.

But cops and other city workers answered by quitting or retiring in droves, and through their unions waged a furious legal battle to block the measure. After years of legal wrangling and with the police force depleted by a third, city and union leaders agreed to a settlement that effectively preserved cost savings that had survived an early court ruling. City voters blessed that deal with approval of Measure F in November.

But San Jose and its taxpayers still are on the hook for an estimated $3.8 billion in unfunded liability in the city’s pension funds and other retirement benefits.

“The voters were not told their money was going to go to pensions,” said San Jose dentist Ernie Giachetti, 75, who voted against the sales tax hike. “If they had been told, I’m sure they would not have voted for the increase.”