ABSTRACT
Difference equations are easy to solve. But they also arise in the context of financial mathematics. Interest on money in a bank account may be compounded more often. For example, an account paying 2% interest compounded biannually would pay half of the 2% every six months. That is, it pays 1% every six months. Biannual compounding serves well to illustrate the idea of more frequent compoundings, but it’s unusual in the real world. Most accounts compound the interest monthly. In order to make smart financial decisions, one do not just need to know some mathematics—one also have to be street smart. In general, determining whether a number is transcendental or algebraic is very difficult. Hilbert stressed the importance of resolving this difficulty by making it the seventh problem in his famous list from 1900.
