What type of estate do a couple have if they are allowed to remain in an apartment on a month-to-month basis after their lease expires?

In this scenario, a couple remaining in an apartment on a month-to-month basis after their lease expires demonstrates a tenancy at will. This type of arrangement gives either party the right to terminate the agreement at any time, as there is no fixed duration for their stay. Month-to-month agreements typically fall under this classification, allowing tenants the flexibility to vacate with appropriate notice while maintaining occupancy with the landlord's implied consent.

Tenancy at will is characterized by its informal nature, often stemming from the continuation of occupancy after a formal lease has ended, which aligns with the couple's situation. The landlord's acceptance of rent on a month-to-month basis also reinforces this arrangement, distinguishing it from more formal lease agreements that specify fixed terms.

In contrast, a tenancy at sufferance would apply if the couple remained without the landlord's permission after the lease ended, while a fixed-term tenancy would involve a specified commencement and termination date. Lastly, periodic tenancy typically pertains to agreements that renew automatically at set intervals, like weekly or monthly, but the term "tenancy at will" better encapsulates the lack of a defined end date and the flexibility of the arrangement in this specific context.