This chapter begins with a study of linear difference equations, which are usually easier to solve in closed form than non-linear ones. A closed-form solution is found for a special type of linear difference equation that arises frequently in problems from finance and economics.

The applications to finance concern interest on loans and the repayment of debt. Hence they should prove just as useful to those who have money and wish to invest it as to those who don't have money and wish to borrow it.

Economists set up mathematical models with which they hope to predict movements in price, interest rates, level of unemployment, and so on. Although some of the economic concepts involved in these models are rather abstract, we have a rough idea of their meaning from everyday usage and this is all that is needed for the models studied in this chapter.

Economic models contain assumptions about the interdependence of the various quantities of interest to economists. A model is regarded as successful if these assumptions lead to reliable forecasts. The quantities studied in economics cannot always be measured with the same accuracy as those studied in the physical sciences and hence economists are more concerned with qualitative predictions — whether the prices will go up or down or whether they will oscillate about some equilibrium value.

Economists often simplify their mathematical models by assuming the functions involved are linear, in the sense of having straight-line graphs.