If a 35 year-old pilot were issued a 1st class medical on January 15, 2012, am I correct that that pilot would be able to exercise privileges requiring a 1st class medical until January 15, 2013? Or would they extend until January 31, 2013? The chart in 14 CFR 61.23 mentions something about it expiring on the last day, but I can't find that exact language anywhere but in the header row of the reference table.
Additionally, after the 1st class medical certificate expires, does it not afford the pilot the privileges of a 2nd class medical for the 60 months listed in 14 CFR 61.23? I'm looking for the part of the FAR that explains how medical certificates of a higher class afford the privileges of a lower class after their original designation period expires.