Interest is rent for the use of money, or, more generically, rent for the use of property (in this case money), just like monthly rent for the use of leased physical premises is rent. So a theory of rents is what you are looking for. You also have to consider the possibility that rent is, or perhaps should be, elemental in the sought for model or system of analysis, such that you are not looking for anything more fundamental, such that rent may be taken as a given and defined is such a manner that lends itself to integration into the crafted system. Perhaps a theory of rents could be set forth like an algebraic structure with starting defined elements, defined operations on the elements, and defined rules of the operations (to insure that it is a closed system not producing elements outside the structure), forming starting axioms from which development of theorems that account for historically observed economic data, may be derived, and from which new attributes of rental systems may be discovered. It may also be found that once, or if, a successful theory of rents is devised, that a slight modification to the structure may reveal a hidden embedded theory of interest on money.