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Do you rent or own? If you rent is apartment in both names, if you own I take it she is not on the mortgage? Her DTI with what you have listed would be well under 45% ($1125) which is what most banks will lend to for a collateralized loan such as an auto loan. Banks will also use gross income, not take home pay to make this calculation. This is assuming she falls into the best risk tier for the particular lender. This is why it can pay to take out the loan with your main bank if they are offering competitive rates as they will use their internal score to help decide what risk level she is on top of info contained in CR.
Background - 6 years in banking, including personal & business credit training, since majoring in Finance.