City officials and community leaders broke ground at the 15th and H Streets NE. crossroads last week, signaling the start of construction on another 167 federally subsidized apartments priced for rental to low and moderate-income families.

But this time, the project's builder, plus the chief economist for the local office of the federal department of Housing and Urban Development and the director of the city's Neighborhood Legal Services Program say that skyrocketing construction and operating costs have priced the units beyond the reach of many of the families for whom they are intended.

The mathematics are simple, oficials say:

The cost of building the units has doubled in the last six years. This is turn means that the rent on each unit - which is pegged at a fraction of construction costs - has also doubled. The income of families qualifying for the housing, however, has not doubled. In some cases, their income has increased only slightly or not at all.

Known as "236" houses because they are built with subsidies provided under Section 236 of the 1968 Housing Act, thousands of the units have been built throughout the nation's inner cities as part of a reconstruction program in the wake of the 1968 urban riots.

"The construction costs have priced the $5,000 to $8,000-income individual out" of the 15th and H Street project, builder Joseph Horning said in a recent interview. "These units are out of reach of people who make below $9,000 a year."

The ability of the program to satisfy the housing needs of those (earning between $5,000 to $8,000 annually) has been impaired," said James T. Smiley, area economist for the local HUD office, as a result of the high costs.

"The 236 program is not a low-in come program any more. It basically has become a middle-income housing program," said Willie Cook, executive director of the Neighborhood Legal Services Program, who specializes in helping poor families with housing problems.

To illustrate what has happened to the program, Horning said he built 109 apartments in Southeast six years ago with financiang from the 236 program. Each of those units cost approximately $11,000 to $12,000 to build, he said, and the rents ranged from $112 to 7142 a month, depending on the apartment size. The rents included utilities.

Hornig said he is using the same plans from the Southeast project to build the H Street apartments with only minor modifications, but each unit will cost somewhere between $23,000 to $25,000.

The rents will range from $157 to $210, and the tenants will have to pay their own utilities, he said.

Since the high costs make it difficult for many low-income residents of the H Street area to afford the apartments, Horning and community leaders have asked HUD to increase from 33 to 50 the number of apartments in the project that can receive a second subsidy.

Under the 236 program, rentare based on what it would cost to pay off the mortgage on a house if the interest rate on that mortgage is 1 per cent. The government thaen subsidizes the difference between the rent and the actual amount needed to pay off the mortgage at the interest rate the builder actually receives from a bank or savings and loan.

Since many low-income families cannot even afford rents based on a 1 per cent mortgage interest rate, the government offers an additional subsidy for usually 20 per cent of the units in a 236 project. The family in one of these apartments pays 25 per cent of its income as rent and the government subsidizes units that Horning and the others want increased.

The 236-program was originally designed to provide housing for families earning too much to qualify for public housing but not enough to afford good housing on the private market.

In 1968, District residents earning $4,860 to $8,100 could qualify for a 236 apartment.

Now an individual can earn as much as $11,300, and a family of eight can earn up to $20,30 a year, and still qualify for the program.

These income eligibility limits have been increased, Smiley said, because "Congress is pushing for more economic intergration."

While many low-income families cannot afford the new apartments, some who live in existing 236 apartments are also having difficulty paying their way because of rent increases.

One of these projects, the 137-unit Immaculate Conception apartments at 1330 7th ST. NW., built by the Immaculate Conception Church and managed by Shannon and Luchs, recently announced a $17 to $24 monthly rent increase proposal. The rents currently range from $190 to $248 a monlth. The proposal increase must be approved by HUD.

Shannon and Luchs told tenants in a letter announcing the proposed increases that additional money was needed to pay higer gas, electricity and water and sewer charges.

Carolyn Palmer, 27, president of the Immaculate Conception apaartment tenants council, said she could pay the rent on her two-bedroom apartment when she moved into the building as one of the original tenants in1974, but no more. Now she receives a $39 a month HUD subsidy because of the increased rents.

"I have no excess money," she said. "I cannot save...Why have a low and moderate-income building wiht Capitol Hill prices?" Her current rent is $215, and the proposed rent is $20 more.

Audrey Jones, 39, mother of five said she left the Lincoln-Wesrmoreland Apartments, another 236 project on 7th Street NW., in November because she couldn't afford her three bedroom unit whose rent had just gone from $214 to $240. She was earning $240 every two weeks at the time, she said.