Final answer:
A pilot can use a third-class medical certificate to exercise private pilot privileges until the end of the month, 5 years after issuance if they are under 40, or 2 years for those over 40 at the time of issuance.
Step-by-step explanation:
A pilot can exercise the privileges of a private pilot certificate under a third-class medical certificate until the end of the month, 5 years after the issue for those under age 40 at the time of the medical certificate's issuance. For those over age 40, the medical certificate's duration is until the end of the month, but only 2 years after issuance. These periods reflect the maximum validity of a third-class medical certificate under the Federal Aviation Administration (FAA) regulations, as stated in Title 14 of the Code of Federal Aviation Regulations (14 CFR) part 61.