You are correct - Pennsylvania law sets the maximum interest rate for a consumer motor vehicle installment contract at 21% APR for cars 2 years or older; for cars less than 2 year's old, the interest rate ceiling is 18%. These rates generally apply to any motor vehicle installment seller, that is, a finance company licensed by PA's department of banking to provide auto financing through a dealership.
A finance company might try to get around these rate caps by offering you a "personal loan" at a higher rate (such as 24%) (maybe less with the car as collateral). A personal loan can theoretically be used for anything, not just an auto purchase. This technical distinction takes the loan out from under the motor vehicle financing interest rate cap. If the "finance company" is a national bank or affiliated with one (there's a good chance that it is), it may not be subject to PA's interest rate laws for small loans because of a legal doctrine called federal preemption.
Sub-prime loans like this are dangerous. Before you enter into this very high interest rate transaction, be sure it's the right move for you. You might want to consider buying less car.
The above is for informational purposes only and does not establish an attorney-client relationship.