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I wanted to share my experience with taking out an auto loan and then about a month later apping for a new credit card and closing an old CL from the same financial institution. My auto loan from my CU was finalized 12/2014, my new Barclaycard was from 1/2015 (I closed an old account with them and opened an Arrival+ as they wouldn't do PC). My score changes for the FICO 08 versions from this site from before these new inquiries and lines to after are as follows:
EQ: 10 point drop
TU: 24 point drop (both the CU and Barclay pulled TU...lucky me)
EX: 14 point drop
All lines, old and new are now reporting, first payment is showing on the auto loan. Length of history is 24 years, AAoA is either 8 or 9 years depending on who you believe (I need to look into that, actually - why is it different?!). I have 9 revolving accounts reporting (most open, a few closed), four installment loans reporting including the new one (auto loans, three PIF, only the new one open), and one mortgage. Oddly, I realized today that though the mortgage dates back to 2005 it only shows as originating in 2013 when I did the most recent refi with the same bank. Huh, who knew?!
I know there has already been a bounce as my TU FICO courtesty of Discover showed a more significant drop to begin with (an additiona 7 points) that have now rebounded. Part of the drop is also likely due to the balances I ran up over the holidays. Althought I PIF, the balances still reported to the CBs. Additionally, I will have three accounts showing balances (my old go-to Visa card which is on hiatus until I meet my Barclay spend, my AmEx which has one autopay on it, and my new Barclaycard cause I want my bonus!) so that will likely have a negative effect in the short term.
It will be most interesting to see if and when I am able to get back to pre-app scores.
I'd be interested to see when you pay down those balances and they get reported: what was the before and current utilization? Also what was were your scores to begin with?
Sounds like you have plenty of tradelines and thickness to your file; you may have crossed an AAOA boundary (work it out with Excel or use credit.com's which is spot on accurate for me from Experian). The original mortgage may have already dropped off some of your files, and it might've dropped off recently too if it was originally from 2005, hard to say without explicit before and after comparison reports.
That's arguably why CK is so godlike for helping diagnose these things, can get down to a week resolution of when a tradeline fell off as unfortunately most of the existing monitoring solutions don't pick that up. The resolution while getting better, still misses a lot unfortunately.

Utilization was about 2x as high this past month as November, around 40% on Chase, about 15% on Target, and less than 1% on AmEx. Overall utiilization was well under 10%, but three cards were showing balances. Target is back to PIF on the current report, as is AmEx, but Chase is still showing that ~40%. It is scheduled to be PIF tomorrow though.
Some additional mortgage info - originated in 2005 and in place through July 2010 with no changes. Refi'd July '10 with the same bank and then again Jan/Feb 2013 - reports say February but we actually did the paperwork in January, so I guess they're showing when it reports. So the original mortgage was in place through 2010 which I thought meant it should still appear. Odd...
The big difference between November and now that I can easily discern are the two HP's on TU, the new loan reporting to all bureaus, and the new CL for Barclay (it's a straight across trade for the account I closed, but the Bean account is closed and the Arrival+ is shows as brandy-new) also accurately shown on all CRs. I'll have to look into the AAoA thing further!