WASHINGTON — The Federal Deposit Insurance Corp. board released a plan Tuesday that would require banks to pay premiums based on their average assets minus tangible equity — a figure roughly equal to their total liabilities — instead of domestic deposits.

The proposal, which has a 45-day comment period, would go into effect in the second quarter of next year.

The Dodd-Frank Act required the change to more accurately capture the insurance risk of large banks, which use a significant amount of nondeposit liabilities in addition to their deposits.

Under the plan, which is intended to bring in the same amount of revenue to the FDIC as before, several large institutions would likely pay a higher price while some small institutions would likely pay less.

To reflect the changes, the agency also proposed a new assessment rate scale. Whereas institutions currently pay between 12 and 45 basis points per their domestic deposits, under the new system they would pay between 5 and 35 basis points per assets minus tangible equity.

Where exactly an institution falls in that range will continue to depend on a complex formula to determine its specific risk to the FDIC.

The agency also reissued a proposal — first released in April — establishing changes in the risk formula for large institutions. The proposal, which has a 45-day comment period, would eliminate certain risk categories and create pricing scorecards for large institutions. The earlier proposal was revised to reflect changes effected by Dodd-Frank.

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