Buying a property with tenants already in it.

[Richard Campbell Jr]

I am closing on a duplex rental property on May 31st. The rent is due on the 5th and on the 15th for each unit. How will the transfer of rent work since I will own the home in the middle of a tenant's pay period? Also, when will the transfer of rent occur? Does that happen on the day of closing? Same question for the security deposit. Will that transfer occur on the day of closing?

Thanks!!!