Despite efforts to contain the cost of medical care for employees, the annual cost of medical benefits increased at an average annual rate of 21 percent from 1987 to 1989, according to a report released yesterday by the Wyatt Co., an international benefits consulting firm.

Based on a survey of more than 900 employer-sponsored medical plans, Wyatt found that 2 out of 3 plans require family contributions. Over the past three years, the average family now pays $1,044 a year toward its health coverage, up from $756 in 1987. Average individual contributions have gone up from $264 to $384.

The study showed that the out-of-pocket limits for employees now average $1,400 for an individual and $2,160 for a family.

But even though it may seem like individuals are paying more for health care, data released yesterday by the Department of Health and Human Services showed that households paid about 61 percent of medical expenses in 1965. By 1989, that share had fallen to 37 percent as business and government paid more of the burden.

HHS Secretary Louis Sullivan said the cost of health care is rising faster than personal income, corporate profits and government revenue.