Chapter 1

# Mathematics of Compounding

## 1.1 Interest and Return

### 1.1.1 Amount Function and Return

Any rational investor prefers a dollar in the pocket today to a dollar in her pocket one year from now. If an investor lends money to a borrower, the investor expects to be compensated for the use of the money. Interest is a compensation that a borrower of capital pays to a lender of capital for its use. If an initial amount P grows to an amount V over time, then the difference I = V − P is interest. This situation is illustrated in Figure 1.1. For investments, it is often called interest earned, but it goes by other names such as return on investment or coupon payment. We assume that a nonnegative amount, and usually a positive amount, of interest is ...