Builder Joseph F. Horning Jr. says he's finding that there is a market for $480-a-month, two-bedroom apartments in Northeast Washington, an area that has seen little multi-family construction in recent years.

Since Horning's project, The Heights, opened quietly in August at 400 Taylor St. NE, it has averaged four rentals a week. The first section of 153 one- and two-bedroom apartments will be completed this winter. A second section will be started in the spring.

The modest-sized apartments sit high on a 13-acre site purchased from the Catholic Marist Society. A mini-mall on the site, which is north of Catholic University, will open next month. It will have convenience food and liquor stores, a restaurant, a dry cleaner and space for two other tenants. The second floor of the L-shaped complex will have 8,000 square feet of office space.

Joe Horning, who operates the Horning Brothers building and management firm with his brother, Lawrence, said that the combination of new, fairly high-priced rental apartments and "the only shopping within a mile or so" seems to be working out well.

"It's a vital area with nearly 10,000 persons within a half-mile radius," he said, "and we are attracting professional persons whose employment bases are conveniently nearby."

The Horning firm is also building the Michigan Park North town houses in upper Northeast. Other housing under construction in the area near Catholic University include the Park Place town houses by LaVay Construction and the Donohoe Companies, the Buchanan Mews detached houses, the University Park duplexs of Stanley Halle Communities Inc. and Eastern Avenue Contemporaries by Froe $99[Words omitted] Fort Lincoln New Town is not far away -- at Bladensburg and South Dakota avenues.

Horning, who has been building apartments in the District and Montgomery County for 20 years, doesn't discount the difficulty of producing rental units in this era of inflated building costs.

"First we got the unzoned ground for a reasonable price ($1 million) and then we were able to obtain HUD approval for 221(d)(4) financing under the tandem plan that subsidizes the permanent financing at a 7 1/2 percent rate," he said.

"We had to convince HUD of the viability of building and renting apartments in this price range. The mini-mall was also a plus because it provides additional income to make apartment rents a bit lower . . . ."

Other than the mortgage-subsidized Latrobe high-rise built (and fully leased) by the National Housing Partnership in downtown, no large market-rent rental projects have been built recently in the District. And relatively few are being created in nearby Maryland and Northern Virginia.

Apartments at The Heights have gas heat, washer-dryers, wall-to-wall carpeting, storm windows, private gate entrances and electronically controlled building entrances.

One-bedroom units, which have 679 square feet, rent for $425. The tenant pays the utility cost, estimated at $36 a month. Two-bedroom units with 902 square feet have 1 1/2 baths and the utility cost is estimated at $42. Three-fourths of the units have two bedrooms.

Horning said that it takes an annual income of $22,000 to qualify to rent a one-bedroom unit and $26, 000 for a two-bedroom apartment. Only about 8 percent of the people who come to see the model apartments actually qualify under the income requirements, he added.

Most two-bedroom units are shared by two working persons, sales people said. So far, the tenant mix is about 50 percent black and white. Only seven tenants have children, the builder said.

Prior to starting The Heights, Horning and members of the development team met with neighbors in the Northeast area, which includes many moderate-rent apartments, duplexes and one-story houses. "It was essential to have neighborhood support before we went to the District building to get R-5-A low-density apartment zoning," Horning said.

In the 1970s, neighborhood opposition to increased traffic helped kill a plan for University Park, which is across the railroad-Metro tracks from The Heights, that called for apartment and town houses. The company instead built low-density, two-family houses.

Collins & Kronstadt, Leahy, Hogan, Collins and Draper designed the four-level Heights buildings, which are entered by bridges. All of the entries have glass walls, and visitors must phone tenants to get inside.

Even though The Heights will not be completed until late in 1981 or early in 1982, developer Horning is already eyeing a 40-acre tract just across Hawaii Avenue from his current project. "It was scheduled to be the site of a new athletic complex for some years but you never can tell," said the builder.