7 day notice to pay or quit after only 2 weeks.

[Alan Howard]

I closed on my first 4 unit almost 2 weeks ago. Three of the units were occupied and I'm currently marketing the 4th unit which I hope to have rented asap. All three tenants signed new leases with me. I used the same terms as the former landlord. I did this because I read somewhere that the new owner had to honor the leases the tenants were under at the time of sale. The lease agreement for one tenant stated they were to pay rent on the 1st and 3rd Friday of each month. Though I thought this was a bit odd, I put those terms in my lease. Well, the 1St Friday has come and gone and I still haven't gotten a payment or response from the tenant. Tomorrow I will serve a 7 day notice for non payment. I feel now that this payment arrangement is problematic because I'll have to start the process over again when and if the tenant pays a partial payment but then is late on the 3rd Friday payment. I see now that this could be more trouble than it's worth. What options do I have? How would other landlord's have handled this situation? Can I modify the lease at this point? Thanks in advance!