Deposits at commercial banks in the Washington area rose 13.67 percent in the last 12 months to a record $16.709 billion on Sept. 30, compared with $14.700 billion a year ago, according to a Washington Post survey.

Banks in all three jurisdictions surveyed -- Washington, Maryland and Virginia -- registered increases in total deposits, with only three local banks showing a decrease in total time and demand deposits from Sept. 30, 1981.

Virginia banks and their branches posted the largest annual increase, a 16.15 percent jump from total net deposits of $3.545 billion in September, 1981, to almost $4.118 billion on Sept. 30 of this year. During the quarter ended Sept. 30, Virginia deposits showed an increase of 1.42 percent, or $57.5 million, from $4.060 billion on June 30.

Maryland banks and their branches showed deposit increases over the last 12 months of 13.14 percent to $4.433 billion, compared with $3.919 billion a year ago. Maryland deposits grew 6.64 percent during the quarter ended Sept. 30, up more than $276 million from the $4.157 billion reported on June 30.

In the District, deposits rose to more than $8.158 billion, up 12.74 percent, from last year's figure of $7.236 billion. The quarterly rise was 1.28 percent, up $103 million from $8.055 billion on June 30.