Friendly Finance Corporation in Baltimore Maryland payoff not reflecting payments made for 18 months Baltimore, Maryland

Most of what you paid up to now was interest. Assuming you had a 5 year loan, payments would be mostly interest for the 1st 30 months, so of your $5166 paid so far, probably close to $4000 was interest, so the payoff amount looks pretty close to your loan, minus the principle part of that $5k you paid. Mortgages work the same way. Many times it isn't even worth paying off a loan after the halfway point because the real interest going forward at that point on what you still owe is much less than the original interest rate. You're in a pickle if you didn't buy GAP insurance.

She had the car for 18 months, and in that 18 months paid $5166.  The original amount was $11,995 and the payoff is now $10,753.  That means it has been reduced by $1242. 

This is how auto loans work.  In the beginning most of the payment will go to Interest, then as the loan is paid down most of the payment goes to Principal.  Depending on the Interest rate it is very possible that only $1242 went to Principal.   This also figures that she paid on time.  If she paid late at any time that will increase the payoff amount because of additional interest and/or late fees.

If another party was at fault then she just needs to make sure that the amount they are offering will pay off the loan balance.  If her insurance is responsible then you have to be more careful.  Most insurance companies pay "Blue Book" value on the car, they don't by default pay the loan balance.  I can almost guarantee you that because the loan is so new she is upside down on this car.  So the value will probably come in low for her car, unless she has additional insurance such as GAP SHE will be responsible for the remaining loan balance.

"  Where did the $5166 go that was made in payments?"

   Are you really mystified by this?   If I had to guess, I think I'd be pretty accurate in saying that about $1,242 went to the priciple and $3,924 went to interest.   Your original loan paperwork should explain all of this.   It looks to me like you agreed to a relatively high interest rate.  Around 20% or so.  If you're going to take out high interest loans, you should expect most of the money to pay for interest.

  On top of that, loan payments will be mostly interest in the first part of the loan period.  It's not until you've spent a few years whittling away at the principle that interest stops being the biggest chunk of your payment.