Is it ever worth it to refinance an auto loan for a higher APR?

Strictly looking at the loan numbers:

• Your original loan was $20,000 at 4.75% for 60 months. That equates to a monthly payment of around $375. You'll pay a total of $2,508 in interest over those 60 months.
• You have $9,000 left, which means about 26 payments remain. You've paid about $2,000 in interest so far.
• If you refinance that $9,000 into a 60-month loan at 5.69% (4.75 + 0.94), your monthly payments drop to around $173 and you'll pay $1,362 in interest. This means you'll have paid an extra $854 in interest total.
• Your $20,000 car now cost you $23,360+.

Factors to consider:

• Your car is now 3+ years old. It's depreciated, meaning it's not worth what you originally paid for it.
• If you choose/need to sell the car, and it's worth less than you have remaining on the loan, are you going to be able to cover the outstanding balance?
• Having an outstanding lien on a vehicle means you have to have more expensive insurance for it. If you paid off the loan in 2 years, you could find some pretty big savings in insurance, dependent on the value of the car and what coverage is required where you live.

One of your concerns was not understanding why the interest rate was higher for the refinance than when you originally purchase. Simply put, interest rates vary over time and having a better credit score now doesn't account for how those rates have changed in the 3 years since you purchased. Anecdotally, I've never found Bank of America rates to be very competitive. You should check with local credit unions if you're set on refinancing. It's also quite likely that the banks' refinance rates (for cars) is reflective of the fact that the collateral is depreciating and the income isn't worth competing for.

Is it ever worth it?

In my opinion, no. You're just putting more money into an asset that won't be worth what you put in.

One argument might be if you have no emergency fund. I'm not making any assumptions about your personal financial situation, but considering how many people don't have emergency funds I think this is worth mentioning in case others find this post. Reducing the monthly expenditures and strictly putting the payment difference into a savings account until you have enough to cover basic living expenses could be a smart move. Once you have the emergency fund in place, then go back to paying off that car loan as fast as you can. However, if your car is currently worth $11,000 or more, I'd vote that you sell the car, take the $2,000 from the sale and buy a well-loved vehicle, save a bunch of money on insurance and get rid of the monthly payment altogether. Then you can put all of that savings into an emergency fund.