Rollover tenant issues starting on first month of ownership

[Meghan Sullivan]

Hello all! So I recently purchased a double unit with tenants occupying it month-to-month without any form of rental agreement. Upon closing, I met with both tenants individually and went over a rental agreement, which they had both agreed to sign, and did so without pressure or time to think.

The first month came and went on February 1st and I have yet to receive a full month's rent from either. One of them (lets call her 'T1') sent a partial in the form of a money order, which I informed her that I was not going to be cashing, via text, until I received the full amount. She said she would be sending it on the 8th, with the agreed upon late fee, so there is still a possibility that I could be getting that within the next couple days. The other tenant (we'll call her 'T2') told me that she won't have the rent until the middle of the month. She has also been informed of the late fee, after having both been given a five day grace period.

My initial thought was that I would wait out the first month to see if T1 was going to send the full amount by the time frame that she claimed she would. If I did not receive it by march 1st I would start the eviction process.

A question I have though, is that if I have the money order in hand from T1, but haven't cashed it yet (sent via mail) am I safe in not having technically accepted a partial rent payment if I haven't cashed it yet? I only ask because if she doesn't pay the remainder I'd possibly like to return her partial payment and start the eviction process so I'm not stuck with this dilemma every month. However, if I wait until March 5th when the next rent will probably be past due, am I safe in assuming that I'm fine in not returning her money order for partial February rent and starting the eviction process based on the missing remainder of rent for February and full missing payment for March?

My thought was similar for T2, but I already assume more than likely that one won't work out, because I'm not going to be dealing with this every month and if she doesn't have rent until the middle of the month now, more than likely I would be. I'd rather eat a month's rent and be able to vet my own tenants, than deal with late payments every month. My hope this that she'll send February's rent before March rent is due and then I'll wait the 5 day grace period until March 5th and start the eviction process if I don't receive anything, but that almost seems like high hopes. How long would you wait for rent before starting the eviction process? Does until the day after the grace period suffice? She already informed me that she was having trouble paying rent in the past, but I wanted to give her a shot since she was already there.

So far this isn't looking promising, but I was warned and semi-prepared going into this. It's also good to note that there was no transferred security deposit so I had included that into the rental agreement, which is to be paid in increments starting March 1st, and due in full by June 1st. I tried to work with them since they were already living there, but it doesn't seem to be working in my favor at all yet.

Thanks for any help I can get. It's my first property and I've done a lot of research, but I'd like to learn from the bigger pockets community.