Refund of rent for the days not lived at the property.

[Ramesh T.]

I have a rental property in the state of WA. My tenant gave a one month of the security deposit when he moved in last year. His start date was Aug 15th, 2019. So every 15th, he used to deposit his rent promptly. He was on a month-to-month basis as we did not get into any contract after the one-year lease term ended.

My tenant gave me a 60-day notice over mobile chat on Aug 31st night, saying he will vacate on Oct 31st. He did not pay me the rent on Oct 15th, so I assume that he intended to use the security deposit as part of the October rent. Technically, he lived at the property till Oct 29th only. 

My question is, a) do I need to arrange his money back for the rest of the days he did not live at the property or b) do I need to arrange the refund based on Oct 31st notice date or c) since it is a month-by-month extension, I don't need to pay him regardless of when he vacated during the month. 

Btw, he did not ask for any refund yet, but I wanted to make sure I am doing things legally.

I really appreciate your response.