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I'm 21, and my father has some credit cards he has had for a long time, say around 15 years. If he added me as an AU, wouldn't it show that 21 year old me has had a credit card for fifteen years in my credit report?
Yes.
Along with all other data in the added account.
That may result in a score boost, and thus help in acquiring new credit.
The rub with AUs is that, while they may be helpful in obtaining new credit from those who rely only or primarily on a peek at your three digit score, if and when you move up to higher levels of requested credit or better terms, creditors are more apt to do a manual review of your credit report.
In seeing that your score is based, at least in part, on credit history that is not yours it may bring into question the entire value of that score in their decision making.
They have no way to "back out" history of single accounts, and thus cannot produce a score that is representative only of your repayment risk.
A great way to build or rebuild when seeking relatively low end credit, but removing the AU may become desirable as your credit improves.