It actually is a little more complicated. Little know fact is that you are NOT APPROVED at the time you drive away and your terms and even lender can change after you take delivery.
Dealerships run your credit and ask your income, and other debts. They take that info an compare it against a list of lenders they work with. Each lender shows their offers (terms, APR) and requirements (down payment %, credit score, DTI%) and restrictions (no BK, no repo, no repo in last 3 years, no lates in last 6 months, etc).
Now many times lenders will have multiple tiers, and multiple terms. A dealership may work with 20-30 lenders and each lender may have 3-4 tiers and each tier have 5+ different terms so there are literally hundreds of options. The finance manager keeps track of all of this for the dealership. The sales manager loads your data and all the loans you don't qualify are excluded. He picks the "best" one based on your requirements and uses that to get you your "monthly payment".
Here is where it gets tricky. When you buy a car you are buying the car. The final sales price is fixed and can't be changed. If the dealer may a "good faith" attempt to secure financing and it falls through then dealer may need to change your financing or even go with another lender.
What does this mean?
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You sign 2 pieces of paper (among 30 others). One is purchase agreement. It shows the exact car (make, model, VIN, odometer, options etc) and break down of price (sales price, minus trade, plus loan payoff, minus rebates, plus tax, title, tag, processing) and the final price. That paper is an agreement to buy this car at this price PERIOD. If financing falls through you are liable for securing your own financing or paying amount in cash (usually within 30 days). All this is buried in that tiny print at bottom of page.
Second paper is truth in lending contract. It shows your financed price (total - down payment), apr, terms, total amount paid, total interest paid, and monthly payments. Buried in this fine print is wording that this is a tentative contract based on final approval from lender.
I sold cars for two years and I would say one out of 5 deals would require re-financing. Someone needs car payment to be $400. I work a deal where it is $399 and it based on 8% APR but the finance manager knows the customer is on the limit of what bank will allow. It is a Saturday (banks aren't open). Customer signs and drives off. On Monday loan app gets submitted. It gets rejected. Finance manager lines up couple of options. New loan at 9% with 10% down ($2800) with new payment of $416 or new loan at 10.5% with payment of $436. Customer is pissed but they have already taken delivery and signed two documents. The purchase agreement requires customer to purchase vehicle PERIOD (even if they need to find their own financing or pay cash). The truth in lending document only states loan is tentative. Customer usually takes the no down payment option and ends up paying higher APR and $36 more a month above their "absolute highest limit".
How to avoid this?
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Get a blank check. Most CU, Capital1, USAA and other lenders off "blank check" program/ Before you go to dealership you submit an app and they approve/disapprove you, give you max loan and APR%. You take check to dealership and between you & dealership it is a cash deal. If dealership can get you better offer you can take their offer. If it falls through you can still use the "blank check".
DON'T RELY ON DEALERSHIP.
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