Three 27-story apartment buildings will be built at 49th and Chicago Beach just north of the present “Indian Village” cluster of elevator apartment buildings, according to plans made public last week by the Draper Kra mer real estate firm. A $17.5 million Federal Hous ing Administration insured loan has been requested for the project which is expected to cost more than $20 million. A total of 1,028 apartments are planned, including 180 studio apartments and 511 one-bedroom, 257 two-bedroom and 77 three bedroom units. Garage space will be provided for 600 cars, Draper Kramer said. The site occupies 3 1/2 acres just west of the outer drive over looking the lake. Architect for the project is Loewenberg Loewenberg, which is also one of the sponsors. Draper Kramer will be in charge of financing, leasing and management of the building. Other sponsors are Reuben Musikantow, Chicago real estate investor; and Snow Walters, Cleveland builder. “We hope to start construction in the spring of 1961, with the first occupancy about May of 1962,” said Maurice A. Pollak, executive vice-president of Dra per Kramer,