Inherited tenant rent increase.

[Account Closed]

I bought a duplex with one side vacant and one tenant with monthly rent of $625. Market Rent is $775. I was able to rent the other vacant unit for $775 with $25/pet monthly rent. The inherited tenant old lease will expire soon. How do I increase rent on the unit to Market Rent without creating artificial turn over? The tenant has 3 cats and I would like to charge $25/pet rent. My state has no rent control law.