  We investigate the time series generated by an elementary and deterministic
financial process that consists in making monthly contributions to a savings
account subjected to the devaluation by a monthly negative real interest rate.
The monthly contribution is a piecewise constant function of the account
balance. We show that a dichotomy holds for such a financial time series:
either the financial time series are asymptotic to finitely many periodic
sequences or the financial time series have an uncountable (Cantor) set of
{\omega}-limit points. We also provide explicit parameters for which the
financial process is chaotic in the sense that the financial time series have
sensitive dependence on initial conditions at points of a Cantor attractor.
