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With your profile, you should have no problems. Why just Wells Fargo and BOA? I am not sure if they will be willing to give you a personal loan that high. Have you looked into Prosper or Lending Club?
You can get a low rate and the money faster than Wells and BOA.
I had a loan with Wells Fargo for my old truck. When I got it I have no idea what my score was, but I was probably around 86% utilization. I'm fairly certain that my FICO would have been below 700 also. They gave me a $15k loan at 2.9% APR. I don't think that was bad at all.
With the information you're giving me, I'd say you have a virtual lock on a decent APR and acceptance with Wells Fargo Auto Finance.
Your financial stats are healthy, you should be able to get a personal loan. I found that credit unions are able to loan at the higher ranges more so than banks, for example, I have a personal line of credit with a credit union for $20,000 whereas private banks only offered something south of $15,000 (but I didn't ask for more since I really didn;t need it, just got it to build a relationship with them and to have it available just in case I do need it).
Lightstream loans offers a variety of options . I recently got approved for a used car loan to use at a dealership. The application process was fast and simple. The great thing about my car loan is that they do not get listed as a lien holder; so its basicly like paying cash to the dealership.
I applied on a Monday around 5:00PM next morning received an email saying I was approved. I completed the application process and the funds were in my bank Thursday .
The was the easiest loan I have ever applied for .
Have you considered the financial institution where you do your personal banking. Also, I would recommend a small community bank or a credit union for better rates. I have a loan with Prosper all though the rate that I received isn't competitive. Prosper also has something similar to a loan origination fee. Thereby, if you apply for 20K, they will deduct 1K and your loan proceeds will be 19K. The 1K is their fee.
Lastly - depending on your borrowing needs, have you also considered a PLOC. I have a PLOC with Citibank. Again considering it is an unsecured line of credit - the rate isn't the best.
Considering your profile, I would think you would have access to multiple options. However, from personsl experience - I would probably say not to waste much time with Wells Fargo. Also, unfortunately - BOA does not offer unsecured loans. Your only option with BOA will be a HELOC.
Best of luck.