Piecewise step function for changing dollar amounts? Visiting the Wikipedia article for continuous functions I found this:

As an example, consider the function h(t), which describes the height
  of a growing flower at time t. This function is continuous. By
  contrast, if M(t) denotes the amount of money in a bank account at
  time t, then the function jumps at each point in time when money is
  deposited or withdrawn, so the function M(t) is discontinuous.

However, a quick investigation of money-, economics-related formulae showed that no function depicts money's innate discreteness (jumping from dollar to next dollar, cent to next cent). Obviously a bank account jumps up or down in dollars/cents, hence, discreteness. But how would you construct such a function. Typically, a discrete function looks like this:
$$
 f(x) = \left\{ \begin{array}{r@{\quad \mathrm{if} \quad}l} 
 1  &  x \geq 0, \\
 \!\! -1  &  x < 0. \end{array} \right.
$$
that is, your classic step function. It seems to me a "money step function" would have to have a condition for literally every dollar -- or my thinking is way off here. So my question is, how can I depict the discrete nature of money jumping up and down by dollar/cent amounts over time?

The jumps come in increments of time, not in increments of dollars.  You can use the floor or ceiling to describe the function.  Say I open a bank account for $100$ that pays $5$ simple interest every year.  Let $t$ be the time in years.  The account value is then $100+5\lfloor t \rfloor$.  You can also use the floor and ceiling to describe the effect of rounding.
