I'm striking through my post as it may well be incorrect!
Hi Anchor,
I believe Guya is correct in this point (no offense at all intended, but this is important not to get confused when people find this post in the future). The instructions on the FBAR form say exactly this:
"Who Must File an FBAR. A United States person that has a financial
interest in or signature authority over foreign financial accounts must file
an FBAR if the aggregate value of the foreign financial accounts
exceeds $10,000 at any time during the calendar year. See General
Definitions, to determine who is a United States person."
So the criteria for filing an FBAR is: if the total aggregate (sum) of all accounts at any (one) time is $10,000 or more, you must file. So in the situation you describe with the $8k and the $4k max values in your post, since the total value is not over $10k at any one time, you do not need to report.
Then, IF you need to file, the number that goes on the FBAR form is the maximum account balance for each account.
It can be a confusing criteria, but don't confuse having to report the max values on the FBAR with needing to use the max values of each account to calculate the $10k threshold. You won't find the wording "Aggregate of max values" anywhere on the FBAR form.
Anyone else, please free to correct this if I'm wrong.
*note I'm not a tax expert, but have spent many dozens of hours looking into this.... [/s]