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You fail to address the first sentence of your homework: you do not have an application class named LetterDemo.

I'm a strong believer in always specifying the access modifier.  Therefore both your Letter and CertifiedLetter classes should be decorated with public.

The name of your properties should be Pascal-cased.  Specifically they should begin with a capital letter, as in Name and Date.  I would suggest that Date is too generic a name, and that you should rename it to SentDate.  Why?  One day you may modify CertifiedLetter to record a ReceivedDateand having clearly named variables adds clarity to your code.

The Name property should only record the actual name, and ditch the preface.  You should omit forcing the user of your class to include "\nSender: ".

Likewise SentDate should omit "\nDate: " and only record the actual date.  Furthermore, the type for this property should be Date and not String.