For Amount Financed we have terms and definitions in 3 topics. The topics are Automotive, Mortgage and Refinance.

The portion of the purchase price that is actually financed. In addition to the cost of the car, it can include the costs of an extended warranty, credit life insurance, and other items rolled into the payments.
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On the Truth in Lending form, the loan amount less "prepaid finance charges", which are lender fees paid at closing. For example, if the loan is for $100,000 and the borrower pays the lender $4,000 in fees, the amount financed is $96,000. A useless number. See Another Truth in Lending Lie.
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The part of a vehicle's cost that a lender supplies. To determine the amount financed, multiply the purchase price by the interest rate; subtract that amount from the purchase price; add state purchase tax to that remainder; then subtract the down payment. Put differently, AF = purchase price - (purchase price X interest rate) + tax - down payment.
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