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To start, let’s consider a loan, which can be in the form of a deposit, a bill or any other money-market instrument. For this loan, an initial amount represented by 𝑋𝑋0 is lent for a period 𝑇𝑇. For instance, 𝑋𝑋0 could be the purchase price of a bill.

Here, 𝑇𝑇 represents the length of the loan in years (e.g., the amount of time between the purchase of a bill and its maturity). If a loan is 3 months long, we would have 𝑇𝑇 = 0.25, as it is a quarter of a year.

Suppose that the promised repayment at time T is denoted 𝑋𝑋𝑇𝑇. This specification is at the core of the loan agreement, indicating how much is lent, for how long, and the amount repaid at the end. One could view this payment 𝑋𝑋𝑇𝑇 as the repayment of the initial loan 𝑋𝑋0 as well as an interest payment of 𝑋𝑋𝑇𝑇−𝑋𝑋0.

It is important to note that some loans have more complicated repayment structures (involving more than one repayment at the end), but these are not important in the money market and are not considered in this module.

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