Existing Tenants/Leases - No Late Fee

[Jordon P.]

Purchased a 3-unit in Pennsylvania October 2018 that was fully occupied and leases in place. Rents were paid a little late in November and mostly on time for December, except for one unit. He texts me today and says he will pay the rent on the 12th and sorry for being late. I said that is fine but the late fees are such and such and that he will be required to pay them. I also stated that I sent him over two letters outlining the late fees (which I did and he acknowledged) within the first two days we took over the property. He replies that his existing lease says nothing about late fees and he flatly refused to pay it. I checked over the lease again and he is right. It does not address late fees anywhere. 

My question is, if the existing lease doesn't mention late fees, am I able to set the policy myself? Should I just process an eviction when he doesn't include the late fees with his payment on the 12th? What is my recourse here? I am hoping that I don't have to wait this out until his lease ends. 

Please reserve comments about not addressing this lease before purchasing the property. The other 2 leases have late fees mentioned, but we overlooked this discrepancy in the due diligence process.