Lender Fees are calculated differently than you think. Instead of taking the Total System Cost Amount and multiplying by the dealer fee, it is instead calculated as such: Total Cost with Fees = System Cost/(1 - dealer fee percentage), where the dealer fee percentage is between 0 and 1. Dealer Fee = Total Cost with Fees - System Cost.
As an example: If a dealer fee is 24.79% (represented as 0.2479) and the System Cost is $25,967.50 then the math is: $25,967.50 / (1-0.2479), or $25,967.50/ 0.7521 which equals $34,526.66. Dealer Fees in this example come up as $34,526.66 (Total Cost with Fees) - $25,967.50 (System Cost) = $8,559.16
It's done this way because the fees have to get tagged onto the principal that is being financed. That way when you take the gross cost times the dealer fee you get back to the net. Otherwise you would be losing money.