Perhaps the most tempting, most nerve-wracking and potentially the most profitable investment for city people is a rundown apartment house in a marginal but improving neighborhood. You can buy sound buildings cheap, fix them up, attract tenants able to pay higher rents, then sell the building at a profit. In the meantime, the rental income covers the costs and yields a modest return.

A young New York City couple -- Linda and Dick -- recently launched themselves into this kind of venture in a shabby neighborhood toward which SoHo, a chic artists' district, is spreading rapidly.

This couple put $14,000 down on a $68,000, 17-unit building -- $500 of their own money and $13,500 borrowed from a close friend for 18 months at 12 percent. For the balance, they assumed an 8 percent mortgage from the former owner. From this point, Linda tells the story:

"Owning a building is definitely a financial venture on which we hope to make money, but it's also an emotional and sociological experience. It has been an education not only in plumbing and furnace, but about human nature and ourselves.

"We found the building through a friend who also invests. I was horrified when I first saw it. No lock on the front door, graffiti on the walls, a urine smell in the halls. But all Dick saw was the good condition of the pipes, the roof, the boiler and the wiring, and the reliability of the rents. He said that a lock, paint and Lysol would fix the rest.

"I attacked this project like a huge research assignment. I drove the lawyer nuts, the accountant nuts, the previous owner nuts, Dick nuts. I arrived everywhere with long lists of questions and wouldn't leave until I got them answered. Then a horrible truth dawned. Some of my questions had no answers. No one could guarantee that we'd make a profit, avoid problems and pay the oil bill. Past a certain point you can learn only by doing.

"Some days are better and some are worse. Today is worse. A truck drove across our sidewalk and it collapsed to the tune of $1,000 in repairs. We've had a lot of unexpected expenses.

"Then there was the day that two different oil companies each claimed to have put 900 gallons into our 1,000-gallon tank.

"Everyone said we'd have trouble with the tenants -- most of them Spanish speaking and about half on fixed incomes from welfare or Social Security. But on the whole they've been wonderful.

"We wrote a letter telling them who we were and what we wanted to do with the building, and asking what repairs they needed. Now, we've made a modest start on improvements. The front door is kept locked. Everyone takes their trash to the back instead of piling it in the front, and there's almost no littering in the halls.

"Dick's stroke of genius was that we should mop the floors ourselves. When the tenants see us working, they work harder to keep the building clean. We've already had an offer to sell for $10,000 more than we paid.

"Three tenants are in the building illegally, but it's a costly and uncertain process to evict them. Welfare tenants qualify for free government legal aid, which means they can fight you indefinitely. We offered two tenants $25 to move and they left. But an artist is holding us up for $1,000 or more.

"My big worry is money. I'll breathe more easily after the first round of rent increases and when our downpayment loan is paid off.

"There's a phonomenal amount of phone calling and paperwork, my job -- and maintenance and renovation -- Dick's job. We've made friends with other building owners in the neighborhood. They're an invaluable source of information on how to get things done.

"Most of the time it seems worth it. Our hearts soar when an art gallery opens around the corner and a nice dress shop, down the block. We hear that three old buildings near us will be completely redone, which is the best sign of all. Just walking around the neighborhood, you can see new life."