Some apartment builders, noting the increasing size of the elderly population here and throughout the United States, are offering a variety of financial incentives to attract senior citizens as tenants, including limited rent increases for the length of a multiyear lease.

NVProperties recently started a rental program for senior citizens and Oxford Development Corp. has had a similar program for several years.

"We feel the senior citizen market is key," said Rick Moore, director of property management for NVProperties in McLean. "It's really sneaking up on property managers."

According to Real Estate Research Corp., the number of people between the age of 60 and 64 is expected to reach 10.6 million in 1990, up more than 5 percent from 1980, and the number between 65 to 74 is expected to jump to 8 million in 1990, up 19 percent from 1980.

At the same time, housing costs, which consume more than 35 percent of monthly income for many senior citizens, are continuing to rise, causing a greater strain on their mostly fixed incomes. While many people over 65 have a great deal of equity in their homes, they may not have much cash and be physically unable to maintain their homes.

"We're trying to encourage older people living in single-family homes to move into apartments," Moore said. "We feel so many senior citizens have lived in homes so long that they don't know what it is not to have to mow the grass or worry about shoveling snow."

The rental programs are designed to help senior citizens keep housing costs affordable and in line with cost-of-living increases.

Under the NVProperties program, tenants who are 62 or older and sign a two-year lease will not be required to pay a security deposit as long as they have a good credit history. Their rent increases will be limited to no more than 3 percent a year. Rent increases normally range from 5 to 8 percent.

At NVProperties' developments, monthly rents start at $725 for a one-bedroom unit and rise to $945 for a three-bedroom unit. If the person becomes ill and moves to a nursing home or moves for any other reason before the lease has expired, NVProperties terminates the lease and the person is not liable for any money, Moore said.

By the end of 1988, the company is planning to start its elderly rent program at nearly 2,000 apartments. Currently, the plan is in effect at Oakton Gable, which has 321 apartments; Windsor Gable at Kingstowne, which has 294 units, and Providence Park, which has 140 units. NVProperties is planning to put the program in effect at its Old Centreville Gable and Woodlawn Gable complexes near Alexandria.

Brian Dapper, regional vice president for Oxford Development Corp., said his firm does not yet have any rental programs for senior citizens in the Washington area, but it does have similar programs at projects in Georgia and North Carolina.

He said the company focuses its efforts on providing additional services and upgrading its apartments.

Through its Oxford Retirement Care Services division, the company develops complexes with single-family homes, apartments, town houses and nursing and medical care facilities for senior citizens. But these are primarily geared to wealthier retirees who may already have a good pension and a large sum of money saved.

Special senior rent programs may entice more elderly citizens to sign multiyear leases.

Leo E. Baldwin, president of Leo Inc., a consultant company specializing in senior housing, long-term care and home equity conversion loans, said many senior citizens are reluctant to sign more than a one-year lease unless they know well in advance that the landlord will not raise rents significantly.

"Sometimes a landlord's expenses may not justify a rent increase," he said.

"But if the landlord owns a piece of property and is in a position to boost the income on that property, he may capriciously raise the rent."