There may be. I have been unable to find such a provision.
Here's a link to the law on late fees. It is only two pages.
https://www.ncleg.gov/EnactedLegisla...2/GS_42-46.pdf
No, the law is...
$1200 x 5% = $60Is due in monthly installments, a landlord may charge a late fee not to exceed fifteen dollars ($15.00) or five percent (5%) of the monthly rent, whichever is greater.
So the fee is within the law. That law is at the very top of the link I posted above.

