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Do I need to write the date on the back of a received check when depositing it?
You do not need to write anything on the second line.  There are a variety of helpful things that you can add, e.g.: For Deposit Only.  This tells the bank to deposit the check into your account and ignore other signatures.   Your account number.  Especially useful when added to "For Deposit Only".   A countersignature.  This tells the bank to pay the check to someone other than you.   Countersigned checks used to be much more common than they are now.  Someone who didn't have a bank account might ask someone who did to cash a check for them.   See also:  Four ways to endorse a check which gives the correct format for endorsing a check in these ways.