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Based on the info. you provided, your wife should be able to get the loan on her own easily.
Thanks for the reply. I appreciate it.
FICO 08 is very solid.
Income of $45,000 / 12 months = $3750 monthly gross income
$3,750 X 40% (0.4) = $1,500 available for all payments showing on credit report. (To meet fairly standard lending criteria)
Very rough guess of $1,100 for minimum payments for House and 3 credit cards listed.
This leaves around $400 for a car payment if the bank wants you to keep your debt to income ratio below 40%
$15,000 loan at 3% for 5 years is $269.53 monthly. My semi-educated guess is that you will be approved.
It may be worth it to see what PenFed.org might do for you on an auto loan. One EQ pull for membership and an auto loan and if you wanted to pick up a credit card as well.
Watch out on that Discover, you are basically at 80% utilization and some lenders will not be happy with that amount.
Good luck and let us know how things work out!