WASHINGTON — The Senate voted Wednesday to let the Federal Reserve slice the fees that stores must pay banks each time a customer swipes a debit card, handing merchants a victory over banks in a lobbying battle over billions in revenue.

Those charges now average 44 cents per transaction and mean $16 billion annually for banks and credit card companies, according to Federal Reserve data.

The Fed has proposed holding those fees to a maximum of 12 cents per swipe. By law a final rule must take effect on July 21.

While it might still be changed, few expect it to differ dramatically from the current proposal.