Inherited Tenants no lease

[Dave Frederick]

Hello! Looking for advice here. I’m closing on a duplex, with an inherited tenant paying way under market value. I think California prevents me from signing a lease for more than a 10% increase. She is paying $900 a month, market is about 2200-2500. There is no lease, the prior owner passed away and this house was sold through a trust. All that exists is the tenants monthly payments. 
 
I understand I cannot terminate a lease without cause, but there is none. I know I can’t sign a lease greater than 10% since there’s a documented a MTM rate. Any advice on my options? I heard I have to give a 60 day notice, but can’t find it in writing. Id keep her if it could charge market rents (current mortgage doesn’t support it), so it looks like I have to let her go. I’m interested in options to make the process smooth and legal.

Does anyone have that statute or law for a 60 day notice? Any advice? I’m considering cash for keys as an option as well.

thanks in advance!