Please explain this loan to me. Not sure where the fee is going in the payments.

I have a loan offer as follows, I can't upload screenshots:

Principal Loan Amount: $18,400

Administration Fee: $1,838.16

Amount Deposited: $16,561.84

Term: 36 Months

APR: 17.19%

Interest Rate: 9.81%

Payments: $592.08 per month

TILA Paperwork Shows:

Annual Percentage Rate: 17.19%

Finance Charge (Dollar amount the credit will cost you): $4,753.13

Amount Financed: $16,561.84

Total Payments: $21,314.97

When I do that math of $592.08 x 36 months, I get the $21,314.97. But where is the admin fee? The paperwork says that the admin fee is subject to interest and part of the Principle Loan Amount. Yet they aren't including it in the monthly payments from the looks of it. I am highly confused.