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AAoA stands for average age of accounts. The way you calculate the average of 15 numbers is to add all 15 numbers together and then divide by 15. If you are averaging 8 numbers, you add those 8 numbers together and divide by 8. Etc.
To compute AAoA you want to take the age (in months) of each of your accounts and add that together, and then divide by the total number of accounts. That gives you the AAoA in months. To make that a figure in years, divide the AAoA in months by 12.
I encourage you to do that by hand (or by using a spreadsheet) so you can watch how it works and so you can confirm that the AAoA really is what you think it is.
Then do it again but you'll have one more account of month 0. That will show you the AAoA impact after the new card appears.
A short cut is this. If you have n accounts now, and an AAoA of X, then the new AAoA after the new account is added will be (n * X) / (n + 1). But it's good to do it the long way I gave you above first, so you can really see what is going on.