The equations of the dynamics of finance are discussed and developed in this short note. One can become so engrossed in spread sheet programming to loose sight of the simple and elegant facts governing many financial systems. The elementary systems of finance are important building blocks for understanding of the more complex systems.
Dynamics can describe phenomenon such as market growth, market saturation, market competition, growth of companies on terms of capital, human power, and money. In this note we focus on the dynamics of money.
To study the dynamics of finance, we use a continuous formulation using differential equations. This allows interest and compounding to be dealt with on a continuous basis and our results are for continuous compounding. Similar formulas and results may be found for the discrete case. A continuous scenario is also choses because it is less common, and the results obtained are theoretically more powerful.