QUOTE
Should I show this on the application?
What does it say on your credit report? More than likley the lender you choose for the transaction is going to make a lending decission based on the use of predictive analysis software (credit scoring). This method derives the majority of its data from your credit report and judgemental analysis will only be employed in the case of marginal report data/credit scores! Regardless of the day of the week, the auto lenders/dealers are usually going to know within minutes whether or not they will extend credit. Any delays will indicate that they are shopping your application around to try and get a better profit margin on the loan!
My advice is before you throw yourself at the feet of the auto dealer for financing, why not check with you local bank or credit union to see what kind of financing they are offering. If you follow this process, knowing before hand that you are already approved, you can then deal as if paying cash! Haggle with the salesman/dealer until you arrive at a cash selling price that is acceptable then call the bank to find out what the deal will cost you in terms of payment. Now, if you want to know what kind of rates the dealer has to offer, you are now dealing with a finite number and the salesman can not unknowingly manipulate the selling price in an attempt to leverage financing in order to improve profit margins.
Michael