More Americans will buy homes and pay more for them as prices rise steadily between now and the year 2000, when the cost of a house is expected to be three times the current figure, the National Association of Realtors said this week.

Despite the higher costs, the home ownership rate is expected to climb by a healthy 3 percentage points to a total of 67.8 percent of the population, according to the association's report on housing demand and financing for the remainder of this century. Costs will climb by 6.5 percent a year, reaching the point where a home that sold for $84,600 in 1985 -- the base year for the NAR's projections -- will cost $212,700 in the year 2000.

U.S. population growth has begun to slow, but the number of households will grow from 86.7 million to 106 million by the year 2000, the report predicted, largely because of an increase in the number of single people buying homes.

Those who buy homes will need $897 billion to finance their purchases by the year 2000, more than double the $409 billion they will require in 1990, the NAR predicted.

However, the passage of the post-World War II baby boom generation through the peak home-buying years and a slowdown in population growth will trigger a downturn in the housing market early in the 21st century, according to John A. Tuccillo, the NAR's chief economist.

"The generation behind the baby boomers is considerably smaller," Tuccillo said. First the rental market will soften, but as this group ages there will be a "much lighter demand" for homes, he said.

After the rapid increases of recent decades, the population is expected to grow at a rate of only 1 percent annually throughout the 1980s. As a result, the major influence on the housing market will shift from increased demand to changing needs as the baby boomers age, the report said.

A more mobile population and changes in "attitudes toward marriage, family and social relationships" during the 1960s and 1970s produced major shifts in housing preferences. As home prices soared and interest rates rose, many buyers turned from the traditional single-family homes with a yard to more affordable town houses, the report said. Apartment buildings were converted to condominiums by the thousands, and many Americans renovated existing houses instead of buying new ones, according to the NAR.

The life styles of many Americans are expected to change by the start of the new century, led by the larger proportion of single people and childless couples among home owners. These shifts could also trigger changes in housing preferences.

Families headed by married couples accounted for 78 percent of all households in the nation in 1950. But the dramatic changes of the 1960s and 1970s reduced their numbers until they made up only 61 percent of the nation's households in 1980.

The most popular types of mortgages will continue to be fixed- and adjustable-rate loans, with variations, Tuccillo said, although he predicted more demand for reverse-annuity mortgages as the number of older Americans increases. With these mortgages, elderly residents who have paid off their mortgages but are short of cash can enter into a sale-leaseback arrangement with a lender, allowing the owner to tap into the home's equity while still living there.

Fifteen-year mortgages may become more popular among owners reaching middle age, Tuccillo said. Many will want to buy another house but will not want to have mortgages to pay during retirement years, he believes. With the decline in family sizes, "family wealth and income may be higher in the future."

The NAR based its predictions on demographic studies by the Joint Center for Housing Studies of Harvard University and the Massachusetts Institute of Technology, which forecast that half of all single people will own homes by 2000 compared with 44.7 percent now.

The number of singles will increase from one-fourth of the population to one-third, it said, while the number of married couples with children will grow by only 5 percent and make up about one-third of the population but 81 percent of them will own their homes. The number of childless couples will increase and their home ownership rate will rise from 82 to 89 percent by 2000, the center predicted.

The joint center also predicted that small- to medium-sized single-family houses will increase by 20 percent in number and make up 5l percent of all owner-occupied housing by the beginning of the 21st century. The number of large homes will increase by 44 percent, to 37 percent of the homes, while condominiums and cooperatives will grow in number but account for a smaller proportion, 6.6 percent, of all owner-occupied homes.

Census Bureau experts made their own predictions, reaching many of the same conclusions as the Harvard-MIT researchers, the NAR reported.

The Center for Urban Policy Research at Rutgers University, however, came to a vastly different conclusion about the future of housing. They predicted that most Americans will no longer delay marriage as many have done in recent years, signaling a return to "more conventional life styles" and a growing proportion of households headed by married couples.

The Harvard study predicts that there will be 288,000 more households at the end of the century than the Census Bureau is forecasting and 2.2 million more than the Rutgers researchers expect. The Harvard figures were chosen by the NAR as a "more reasonable" basis for its own predictions about future housing trends, the report said.

The association predicted sales of 6.7 million housing units between 1985 and 2000. Projections for sales and the price increases of about 6.5 percent a year "assumes that home buyers' incomes increase at about the same rate," according to the report. A long recession or downturn in the housing market like that of the early 1980s could reduce sales dramatically.