How do they calculate what your monthly auto loan payment will be?

So, I recently bought a new vehicle and was wondering how my monthly payments were figured out. After digging around a bit, I found this site where a high school teacher has posted the formula as an exercise for her students. Not only that, but I stumbled across this other website where I could find simple solutions to the most of my financial woes.

Well, I thought I would share this gem in case anybody else is interested.

\frac{P(\frac{i}{12})}{(1-(1+\frac{i}{12})^{-n})}  

You can go to this site and the Almighty Internet will give you the same answer.

Alternatively, you can download this document I made in Open Office Calc (free) and see, with your own eyes, what’s going on.

I would love to know, if anyone ever reads this, how the initial finance charge is decided. I thought about it, fruitlessly, until my brain hurt.

Here is the problem:
You have a principal amount of $4049.00. Your finance charge is calculated to be $538.12. Your interest rate is 8.29%. What formula was used to arrive at the value $538.12?

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