Los Angeles-based Farmers Group has agreed to cut rates and issue rebates totaling $100 million to its auto insurance policyholders, Farmers executives and state regulators announced Tuesday.

Under the agreement announced at a press conference in downtown Los Angeles, Farmers will give customers of one of its companies, Farmers Insurance Exchange, a one-time rebate of about $50 per vehicle, for a total of about $32 million. The rebate will apply to customers renewing policies between July 15, 2010 and Jan. 15, 2011.

Farmers Insurance Exchange customers will also receive ongoing rate cuts of about 15 percent, worth an estimated total of about $72 million.

The agreement brings Farmers Insurance Exchange into compliance with the state Department of Insurance auto rating regulations. Farmers’ other auto insurance carrier in the state, Mid-Century Insurance Co., previously cut its rates to comply with the regulations. Mid-Century insures about 1.4 million vehicles in California; Farmers Insurance Exchange insures about 640,000 vehicles in the state.

Farmers Group is a subsidiary of Zurich Financial Services Group.