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It doesn't indicate much of anything, because it's a pretty standard way of ending a letter.

It indicates the writer is probably not a teenager.

It indicates the writer can't spell. Emotion: stick out tongue

It depends on who you're writing the letter to. If, of course, you are writing a personal letter to a friend, then yes- it is okay to close a letter with "Forever your friend, Penny."

If you are writing a business letter, it's probably best to go with a more professional closing.
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yes penny it is ok to close a letter with forever your friend!