Buying rental with tenants middle of the month

[Sarmad Abbas]

Hi folks,

First of all I want to thank @Joshua Dorkin and @Brandon Turner for the fantastic podcast they host. I have learned so much from it and it keeps me motivated. Because of the podcast and this website and BP community I have reached a point where I will be closing on my second rental property but first real deal (first one was a forced rental, was upside down on the town house so had to rent it out a few years ago, luckily it breaks even). 

My question is around taking over a lease, I will acquire the property middle of the month with renters living in the duplex. Would the rent be split between me and the seller because it's mid month, how should I approach this? Please let me know. Thanks.

Sarmad