I agree with Hart CO's excellent answer; you are much better off financially in your current situation than if you consolidate as stated. If they are willing to give you a loan for $37.5K at 11.59% for 4 years, then I can't think of a good reason they wouldn't be willing to give you the same terms for just $6.3K instead. I would ask them for the smaller amount and leave your large loan intact. If they say no, please share the reason they provide.
Update: Based on the new information in your comment, it looks like you can get the loan for $6,300, but at a higher rate of 12.89%. Or you can take out the loan for $10,000 and get the 11.59%. (Presumably because the bank wants to make a minimum profit to originate the loan for you.) Given this, it does make sense to take the smaller loan (unless there is a high origination fee or early payoff fee). Now let's calculate which is better: 6300 at 12.89% or 10K at 11.59%:
- Interest paid on $6300 at 12.89% for 4 years: $1,796.13
- Interest paid on $10000 at 11.59% for 4 years: $2543.83. But if you get $10k, you'll be able to pay off $3700 from your larger loan, so you'll save the interest on $3700 at 9.24% for 3.5 years: $644.59. Total adjusted cost of the $10k loan: $1899.24.
Update Conclusion: the $6300 loan at 12.89% is slightly better (by about $100) than $10K at 11.59%. I'd recommend refinancing just the $6300 on the CC for 12.89%. (Note this is still contingent on low origination fees and no early payoff fees.)
Regardless of what you do, try to throw as much as you can at the higher interest rate loan every month until it's gone. The faster you can pay off the CC, the more money you save, and yes, it should also increase your credit score a little bit due to the lower utilization percentage.
As a side note, I want to comment on this:
My major motivating factor for considering the consolidation loan is to have 1 payment...
I definitely get that, but right now you have 2 payments per month instead of 1. It must be worth a few minutes per month to save $1500. Or you can automate the regular payment amounts and then you don't have to lift a finger, except when you login to make additional payments on the CC, but those payments are enjoyable!