Finding interest rates with fractional banking is very difficult because it is governed by quantifiable and unquantifiable factors.
Regulatory requirements (like reserve ratios and capital requirements) are objective and quantifiable and play a role (but it varies from bank to bank).
The supply of base money is only limited and is another objective quantifiable component.
But...a major component of banking is trust. If I create a new money "exchangepesos" and nobody wants it, then any quantifiable math equation would be useless. Banks create money. They create "deposit dollars" that of course exceed government dollars (base money). For this to work, there must be trust. If I as a depositor or as another bank don't trust say "Bank A", we won't trust in turn their deposit money which will ruin their credit rating and result in the destruction of their deposit money.
Another way of putting this is that banks operate by maturity mismatching. Matching short term debt to long term assets. This is naturally exceedingly risk and depends on those lending short term to the bank to consistently roll over such debt. Because long term assets are long term they will not get the principal in time to satisfy a redemption run by short term debt holders (many of which could be called depositors).
The extent to which a bank can create money and buy interest bearing assets (which affects interest rates) is a function largely of the trust the individuals (but mostly other banks) have in the bank that does the money creation. This is of course non-quantifiable.
The best solution IMO is to at least quantify the extent to which a bank mismatches debt to asset maturities. This is an obscure but growing measurement sometimes referred to as the liquidity mismatch index.
A most practical manifestation of this equation would be to have a graph with the horizontal access being maturity times (say 1 second 'aka demand deposits), 1 month, 1 year, 5 years, 10 years, 25 years, etc...). Then the vertical axis quantify be amounts in dollars. Two lines would be drawn...one for bank debt stratified by maturity time and another for bank assets stratified by maturity time. Measuring the area of the difference of the two lines would give you a relatively interesting idea of where the banking system is at and where it could go (especially when compared to historic norms). But ultimately an exact equation to find interest rates is not possible because trust is so important to banking yet is not quantifiable.