How to find interest rates with fractional reserve banking? As I understand it, interest rates are set by supply and demand, like any price. Money can be thought of like any other finite commodity. Lenders are willing to supply a certain amount of money at each interest rate, and borrowers are willing to borrow a certain amount at each interest rate. The rate can be calculated by setting supply equal to demand.

However, with fractional reserve banking, this picture seems to fall apart. While the demand curve can still be found, the supply of money is not so easy to quantify. If the reserve requirement were low enough, banks could loan out an arbitrarily large finite amount of money. The only limit to the money supply is the reserve requirement. It doesn't make as much sense to say here that the interest rate is set by supply and demand. 

I see a two possibilities:
1) There is a supply curve that depends on the reserve requirement. This means that the interest rate would be a function of the reserve requirement.

2) There is no supply curve. As far as I know, no one sets interest rates (the Fed included, since they only influence rates via open market operations: if they didn't do anything there would still be an interest rate). How can interest rates be calculated in this case?
This question is sufficiently confused about basic concepts that I'm reluctant to go through the effort of clarifying everything enough to provide a meaningful answer, but here is a quick stab...

First, you need to understand that interest rates are not set by the supply of cash provided by banks and the demand from borrowers. They're set in money markets, which is the other side of the credit intermediation that banks perform. Banks lend to borrowers and borrow in money markets (if they didn't borrow, then it wouldn't be fractional reserve banking) to fund a significant portion of their lending.

Second, reserve requirements are far from the only constraint on bank money creation, and I frankly cannot think of a single bank for which they're the binding constraint. Banks are more likely to be constrained by risk-weighted capital requirements, the liquidity coverage ratio, or stress test scenarios than by reserve requirements.

So to answer your question as to how interest rates are determined under fractional reserve banking: bank demand for funds is determined by their set of profitable lending opportunities under a set of constraints including capital requirements (and they face some competition for these funds from firms that have direct access to capital markets and which issue short-term liabilities), while the supply of funds is determined by the amount of uncommitted cash held by firms (and to a much lesser extent, households). These intersect at some point, which determines the interest rate. The Fed affects the risk-free rate by engaging in transactions which swap safe, usually interest-bearing collateral for cash, affecting the relative supply of each.