Frederick Jones and Ping Wong are both over 85; both live on fixed incomes; and both have health problems that limit their mobility. From there, their lives diverge in ways that illuminate the uneven challenges facing New York’s oldest old.

Mr. Jones, 88, did everything he could to secure a comfortable retirement. He worked for nearly 35 years for the City of New York, retiring with substantial savings and a union pension and Social Security benefits adding up to $3,000 a month. Ms. Wong, 90, never had the opportunity to save for her old age. She worked part time for below the minimum wage at a doctor’s office in Chinatown, earning $500 to $700 a month. Her retirement income, including food stamps, comes to about a third of Mr. Jones’s.

Yet the differences in their lives are not what one might expect. Because her income is so low, Ms. Wong qualified for a subsidized apartment in an elevator building near Gramercy Park, where she pays roughly $200 a month in rent and spends her days playing mah-jongg with friends in the downstairs activity room. A home attendant comes for seven hours a day, cleaning and cooking and running errands, at no charge to Ms. Wong. Until recently, when Ms. Wong decided she did not like the food, she received food seven days a week from CityMeals-on-Wheels, which asks only for a voluntary donation. She never worries about money, she said.

“It’s very cheap for low-income people,” she said.

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Frederick Jones has returned to his Brooklyn apartment from a rehabilitation center. Parts of two of his toes have been amputated. Credit Nicole Bengiveno/The New York Times

Mr. Jones, in contrast, falls into what has been called a doughnut hole: He earns too much money to be eligible for most government subsidies, but not enough to pay for the services that would make his old age comfortable. Though he pays only $300 a month for a rent-controlled apartment in Crown Heights, Brooklyn, the building has no elevator and the low rent has become a trap. Mr. Jones had parts of two toes amputated this summer, making the 36 stairs to his third-floor apartment a grueling test. Cleaning and cooking are almost beyond him; on my last visit, I changed two light bulbs for him because he could not get up on a ladder.

Mr. Jones could afford to pay somewhat more in rent. But rents in his neighborhood have risen sharply, to an average of $1,991 for a one-bedroom apartment, according to the Brooklyn real estate brokerage MNS. Walk-ups in the building next door were recently advertised for $1,500 a month. And hiring a home attendant for even a couple of hours a day would eat up a third of his income. For now, he said recently, after a long and slow ascent up the stairs, he is stuck.

“Every time they come out with a new benefit for the elderly, it’s for people who make less than me, so that’s the end of it,” Mr. Jones said.

“They built a new building for the elderly about two blocks from where my daughter lives, so that was great. She said, please take that apartment.”

But Mr. Jones said the building was only for people with incomes below $15,000 a year. “And thank God I got a little more than that,” he said.

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Mr. Jones and Ms. Wong are among the six New Yorkers over age 85 whom I have been following since the beginning of the year. They represent one of the fastest-growing age groups in New York, nearly doubling in number since 1980 — healthier, better educated and more independent than any like cohort before them. Many never planned to live this long, or to navigate a financial landscape as confounding as the one they are in now.

In their lifetimes they have seen Social Security and Medicare greatly reduce poverty among older people. But in New York today, they face a challenge of prosperity. The boom in housing prices has left many of them vulnerable, often clinging to apartments that are no longer suitable for their aging bodies.

“People end up as prisoners in their own home,” said Donna M. Corrado, commissioner of the city’s Department for the Aging. Even the real estate winners — those who bought cheaply, before the market took off — now face rising property taxes that may overwhelm their fixed incomes. And older tenants with low rents are prime targets for unscrupulous landlords, who want them to move out so they can raise the apartments to market rates. “It’s a vicious cycle, and greater in New York than anywhere else,” Ms. Corrado said.

One result has been to drive relatively healthy people into nursing homes, where Medicaid picks up the tab for eligible seniors, said Daniel Reingold, president and chief executive of the nonprofit RiverSpring Health, which operates the Hebrew Home at Riverdale in the Bronx.

“You have people in our facility, you say, why are they here?” Mr. Reingold said. “They seem to be in good shape. They lived in a three-story walk-up, or they outlived their money. They’re coming to a nursing home because they can’t afford their housing or there is no available housing.”

Some don’t have this option. Typically, about 2,000 people age 60 and up stay over in the city’s homeless shelters, according to the nonprofit group LiveOn NY, which works on behalf of senior centers.

Mayor Bill de Blasio has promised to build or preserve 10,000 units of affordable housing for the elderly and 1,000 units for homeless seniors. Mr. de Blasio also expanded a rent freeze for eligible people age 62 and over.

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Ping Wong in a senior complex near Gramercy Park, where she has an elevator and a home attendant five days a week who also prepares lunch and dinner for her. Credit Nicole Bengiveno/The New York Times

But there is a lot of catching up to do. Of the 165,000 units of affordable housing created or preserved in the last decade of the Bloomberg administration, only about 3,600 were earmarked for low-income older people, mostly under a federal program that was vastly curtailed in 2010, according to LiveOn.

At Ms. Wong’s building near Gramercy Park, where rents are set at 30 percent of a tenant’s income, the waiting list for apartments has been closed almost since the building opened 10 years ago, because so many people applied for the 70 apartments, said Philip Deans, the housing manager for Cabrini Apartments, a part of the nonprofit Cabrini Elder Care.

“I’m still working from that original list,” Mr. Deans said. “Every week I receive walk-ins or phone calls from children in crisis mode: ‘What can I do? Where can I go?’”

A comparable subsidized building that opened in Queens three years ago received more than 2,700 applications for 66 units.

On a recent afternoon, Mr. Jones sat on a couch piled with incomprehensible bills and statements that had accrued during his two-month convalescence in a rehabilitation center after foot surgery. Most of the medical bills are covered by Medicare or his supplemental insurance, but a few of them — $50 for an ambulance he didn’t want, late fees for utility or credit card bills he wasn’t home to receive — require him to pay. Such bills can add up: After age 85, the average Medicare beneficiary has nearly $8,200 a year in out-of-pocket medical expenses and premiums, according to the Kaiser Family Foundation.

Mr. Jones was not dismayed. He never is. “Oh no, I don’t have any money worries, thank God,” he said. “I have none. My only money worries are, keep the ladies away from it.”

He opened a folder of photos from his younger days: sporting a double-breasted suit and flared pocket handkerchief, or in a boxer’s stance, with a bushy mustache curling rakishly down around his upper lip. They are portraits of a player in full plumage.

I asked him when in his life he was happiest.

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85 and Up

    “Right now,” he said without hesitation. “I have health problems, but it’s been going on a long time, so it’s secondary. But I think happiness really is what’s going on at a particular time. I used to think happiness was something that somebody brought to you. But happiness, as opposed to enjoyment, is when you are doing something and you are elated.”

    Mr. Jones was born in 1927, two years before the start of the Great Depression, and lost his father, to a burst appendix, before his third birthday. His mother supported the family in Norfolk, Va., as a seamstress.

    “My mother took care of my grandmother, my brother, myself and herself, and she was making $25 a week,” Mr. Jones said. “I say, man, money is worth nothing these days.” He said he never knew he was poor until he was 16 or 17, when he read about how other people lived.

    After serving overseas during World War II, he attended Virginia State University for free on the G.I. Bill, and when he got to New York, an older man steered him toward the civil service. “He said, ‘If you don’t want to ever be on the unemployment line, work for the city, state or federal government, don’t steal anything, and you got it made.’ And that was true.”

    On his couch, Mr. Jones smiled at the memories. An old bicycle, unused since 1967, stood between the couch and a metal window gate. A working television rested atop a nonworking one that Mr. Jones would like to sell. He does not have cable.

    The apartment’s intercom has not worked for close to a year, so if any visitors come, Mr. Jones has to either walk downstairs or hope they’ll wait until someone opens the front door. Last year he successfully sued his landlord to get handrails on the staircase. Mr. Jones said the landlord had no incentive to make him comfortable.

    He often skips meals because it is too much trouble to shop and cook, he said. If there are services available to him, he is not aware of them, and as more public information migrates to the Internet, it might as well be on Mars.

    Yet in many ways he is fortunate to have the apartment. Seniors in New York pay the highest share of their income on rent: nearly 58 percent for single elderly renters, compared with 34 percent for average households, according to a 2011 survey by the Department of Housing and Development.

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    Ms. Wong, 90, plays mah-jongg every day with other residents in federally subsidized housing for low-income seniors on East 19th Street in Manhattan. Credit Nicole Bengiveno/The New York Times

    And the building has its advantages, Mr. Jones said. Neighbors check in on him or help carry things up the stairs.

    “When I retired, my purpose was to make friends, get all the retirement money that I could and move from where I am now,” he said. “But I never did it. When you get hung up between cheap rent in a bad place and expensive rent in a better place, you say, this is not that good, but I’ve been here for certain years, and I keep talking myself into staying here. When people say they’re paying a thousand dollars a month rent, I don’t raise an eyebrow, ’cause that’s what’s going on now.”

    In the activity room at Cabrini Apartments, Ping Wong expounded on her good fortune, with one complaint. Ms. Wong walks stiffly after replacement surgery on both hips and has arthritis pain in her arms and legs. One of her neighbors, who is two years younger than she is, receives more hours from her home attendant.

    “I need more hours, not just seven hours,” Ms. Wong said. “I’m older than her, so I should have more time. My home attendant comes at 11 o’clock and leaves at 6. I have too many things to do myself in the morning.”

    Mr. Deans, the housing manager, said Ms. Wong was “about average” at taking advantage of available public services. “She’s aware of it but doesn’t know how to tap into it,” he said. But she is very sociable and seeks out the building’s social workers, he said.

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    Know Someone 85 or older?

    We’re looking for 15-second videos answering the age-old question: What is the secret to a long life? Your subject can be a friend, relative or acquaintance — or maybe it’s you, but the answer must come from someone 85 and older.

    Record your person's answer and post the video on Instagram with the hashtag #NYTlonglife, or you can email your 15-second video to cityroom@nytimes.com. Remember to include his or her name, age and hometown in your caption. We may include your video in a future project on nytimes.com. The deadline is Nov. 30.

    Immigrants like Ms. Wong now make up nearly half of New York’s senior population, and 40 percent of those age 85 and over — even as the population of native-born seniors has declined over the last decade, according to the Center for an Urban Future, a research group. These immigrants face particular financial challenges as they age, especially those who arrived too late to earn substantial pension or Social Security benefits. Chinese-born immigrants over age 65 are among the poorest, with a median income of $7,000, compared with $18,300 for their native-born peers.

    Ms. Wong grew up in Hong Kong, one of five sisters born to a successful home builder. When she finished high school, she said, her father wanted help working with English-speaking clients, so he sent her to London for a year to learn the language.

    But when she immigrated to the United States in 1982, her limited English skills kept her in low-wage jobs, and her husband died before earning more than minimal Social Security survivor benefits. She worked until she was nearly 80, commuting from Staten Island to Chinatown in Manhattan, until she began to fear she would be knocked down in the crowded city buses.

    These days, Ms. Wong economizes by not buying clothing, and stretches her $200 monthly food stamps by sending her home attendant to Chinatown to shop. She gets cheap prescription drug coverage through AARP, and uses a cellphone provided by her daughter. With her meager savings, she managed to buy a $20,000 burial insurance policy, so she would not burden her daughter.

    A few years ago her daughter gave her a laptop so she could communicate with her grandchildren in China, but the machine was too heavy for Ms. Wong to move around the apartment, and when they tried a tablet, Ms. Wong’s hands shook too much to work the touchscreen.

    Ms. Wong thinks often about money, and what she thinks is: People should spend it while they’re young — travel the world, enjoy life. “What’s the use keeping money in the bank?” she said. “Not to keep it for descendants. They have their own salary. I need not take care of them. They should take care of me.”

    She added: “I’m not the elderly person keeping the money in the quilt or the refrigerator. I like to spend.”

    Her daughter, Elaine Gin, who lives in New Jersey, handles her Social Security checks and bills, and allots her $200 each month in spending money, as well as occasional sums from her own accounts. “I couldn’t go to the bank to withdraw money,” Ms. Wong said. “She tells me how much I spend, how much is left. If I need money to give to people here, she gives it to me.” Ms. Wong thinks a bigger tip to her home attendant’s agency this Christmas will get her approved for more hours.

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    Ruth Willig, 92, at her apartment in the Sunrise Living nursing home in Sheepshead Bay, Brooklyn. Credit Nicole Bengiveno/The New York Times

    Toward the other end of the economic spectrum are New Yorkers like Ruth Willig, 92, who pays more than $5,000 a month to live in an assisted living center in Sheepshead Bay, Brooklyn. Ms. Willig, who worked as a microbiologist, never handled her investments until her husband died 20 years ago, leaving her with a broker whose conversation she says she does not always understand. “But he’s done well for me,” she said.

    Yet Ms. Willig, too, has been buffeted by the economy. Last year she had to leave her assisted living home in Park Slope, Brooklyn, when the owner abruptly announced plans to close it. (A few residents are still living there, under degraded conditions.)

    Reared in Brownsville during the Depression, Ms. Willig was always cautious with money. She and her husband took the family on vacations, but in tent trailers rather than hotels. They sent their four children to college, but to state schools. “There were times when to write the check we had to wait for the next income,” she said. “But I really don’t think I was worrying that much about it. He tried to keep me informed, but I really didn’t pay that much attention.”

    When her friends from the Park Slope center moved to a comparable building in Lower Manhattan, she chose Sheepshead Bay instead, in part because it was less expensive. She misses her friends.

    On a recent morning in her tidy one-bedroom apartment, Ms. Willig talked about something she called “my dilemma.” She wore a neat T-shirt that she had put off ironing because it hurts her to bend to plug in the iron, the sort of small task that is getting harder every year. Her dilemma was whether to endure the pain or hire an attendant, which can grow increasingly expensive. She did not want to outlive her savings.

    “Then I think, what do I need all this money for?” she said. “My daughter says, Ma, you never know what’s going to take place in your life, which is true. So I force myself to take care of the apartment. And I’m able to, thank God. It’s not as neat as I’d like it to be.”

    For now, she was secure, she said.

    Sun poured into the apartment, and the bay shimmered outside. “I didn’t think I’d be so comfortable,” she said. “It shocks me.”