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I have heard installment loans only make up around 10% of your FICO. If you don't have any existing installment loans now, then an auto loan will probably help. The auto loan is going to help the most with future auto enhanced scores as positive auto loan history is highly regarded when trying to get the best rates and terms.
That being said, your scores of 550 - 570 may limit your lender choices more than you expect and result in a loan rate of anywhere between 10 - 20%. This is not a loan you want to have very long. Since you have $6000 in cash, I'd look for a $6,000 loan and pay it off in 6 or less months to minimize the interest penalty.
Whoever you get a loan through you need to make sure there is no prepayment penalty!!! Last thing you need is to owe several grand more for the car due to some clause in your loan agreement.
To pay interest just to build an installment loan account. I wouldn't do it. It factors in at 10%.
I bought my current car with cash. I do have 2 other installment loans though. But, without a current car loan, I have been improving my credit just fine with mostly revolving accounts. My GTI is awesome!