  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.
