During $2024,$ Faith Company discovered that the ending inventories reported on its financial statements were incorrect by the following amounts: $2022$ $$12,000$ understated $2023$ $$28,000$ overstated Faith uses the periodic inventory system to ascertain year$-$end quantities that are converted to dollar amounts using the FIFO cost method. Prior to any adjustments for these errors and ignoring income taxes, Faith's retained earnings at January $1,2024,$ would be: $$ Correct $$ $$40,000$ overstated. $$ $$28,000$ overstated. $$ $$16,000$ overstated.