The decade's lowest mortgage rates pushed sales of existing homes in April to their fastest clip in 6 1/2 years, yielding the largest annual increase in median prices since 1981, an industry survey said yesterday.

Those sales increased 11.3 percent from March to April for a seasonally adjusted annual rate of 3.56 million units, according to the National Association of Realtors' monthly survey.

The April pace of home sales was 17.9 percent faster than the April 1985 rate of 3.02 million units, the Realtors said. It was also the fastest annual rate since October 1979, when homes were selling at a pace of 3.77 million units.

The median price for an existing single-family home increased $1,300 last month to $81,100 -- up 8.4 percent from the April 1985 median of $74,800. The median is the point at which half the homes sold for more and half for less. That annual increase was the biggest appreciation in values for existing homes since February 1981, when median prices jumped 8.6 percent from February 1980.

Interest rates, now hovering above 10 percent for conventional mortgages and 9.5 percent for Federal Housing Administration loans, were said to be the major factor in the spurt in home sales.