General Balance Functions in the Theory of Interest

We develop an axiomatic theory of balance functions (future value functions) in the theory of interest that is derived from financial considerations and which applies to general regulated payment streams, including continuous payment streams. Balance functions exist and are unique up to an initial choice of deposit and investment accumulation functions. In terms of these balance functions we also construct a unique internal rate of return for each regulated payment stream that is an investment project. This theory subsumes and clarifies previous theories of internal rate of return functions for more specialized classes of investment projects.