There is no State Regulation requiring that landlords pay tenants interest on their security deposits. However, many cities have such a regulation. The list keeps changing but some of the cities include Berkeley, Los Angeles, Hayward, San Francisco, Santa Cruz, Santa Monica, Watsonville and beautiful West Hollywood. If you have a rental in California, you might check with your City Officials to determine their rules.
The interest rate keeps changing yearly and with the interest rates so low at this time the amounts landlords will pay is not exorbitant. For example, I believe the LA interest this year is .06% which is less than 1%. On a $6,000.00 security deposit the amount of interest would be $36 dollars.