The mature pension fund, projected by computer, usually grows exponentially with time. Furthermore, the important characteristics of the mature fund (e.g. age structure and relative salary levels, contributions and benefits) tend to be stable. Matrix analysis allows us to predict the form of stability and the rate of exponential growth. The theoretical results in this paper are probably of limited practical value. However, they do provide rigorous explanations for empirical results observed by members of the profession using projection techniques.