You purchased a used car for $15,867.00 plus 5.25% sales tax. The down payment is 10% of the total cost and you have a credit rating of 5.40%. What is your principal balance at the start of the loan.
The total cost of the car, including sales tax, is $15,867.00 + $15,867.00 * 5.25% = $16,706.78.
The down payment is 10% of the total cost, which is $16,706.78 * 10% = $1,670.68.
Therefore, the principal balance at the start of the loan is $16,706.78 - $1,670.68 = $15,036.10. Answer: \boxed{15,036.10}.