Final answer:
The $1,000,000 gift to the City of Matthews, with restrictions to use only interest earned for athletic facilities, should be recorded in the Permanent Fund.
Step-by-step explanation:
The gift received by the City of Matthews from Rebecca Smith is meant to generate earnings that will be used to maintain or improve city-owned athletic facilities. Since the principal must remain intact and only the earnings can be used, the most appropriate fund to account for this gift is the Permanent Fund. This fund is used to account for resources that are legally restricted to the extent that only earnings, and not principal, may be used for purposes that support the reporting government's programs—that is, for the benefit of the public.