Dear Sunil, as per Section 194A, the above condition is within the ambit of TDS provisions, if the payment is not done by an individual or HUF. Hence, TDS would be applicable on payment of interest on car loan to private finance company not being not being the banking company to which the Banking Regulation Act, 1949 applies.
For reference, see extract: Section 194A INTEREST OTHER THAN "INTEREST ON SECURITIES". (1) Any person, not being an individual or a Hindu undivided family, who is responsible for paying to a resident any income by way of interest other than income by way of interest on securities, shall, at the time of credit of such income to the account of the payee or at the time of payment thereof in cash or by issue of a cheque or draft or by any other mode, whichever is earlier, deduct income-tax thereon at the rates in force.