Quantitative Finance

Chapter 5

Repaying Loans over Time

5.1 CHAPTER SUMMARY

In this chapter, we investigate a very simple financial instrument—a loan—using relatively sophisticated tools and thought processes. We are building the mental framework to look at much more complicated financial instruments in the right way. After a short introduction in Section 5.2, a spreadsheet to solve the problem is created in Section 5.3. We see that we can solve the problem by guessing a payment and then adapting the size of this payment until the mortgage is paid off. This idea of selecting a financial control variable to make something vanish is, as we will see later in the book, very powerful in modern mathematical finance. Then, in Section 5.4, a difference equation-based approach ...