Time Value of Money and Interest Rates › Time Value of Money and Interest Rates

When the applicable discount rate is positive and the cash flows are otherwise comparable, a dollar today is worth more than a dollar tomorrow. This ordering connects calculations used to price bonds, value companies, structure mortgages, and plan for retirement. The concept is called the time value of money (TVM), and it is a recurring foundation in quantitative finance.

Why can money be worth more today? An investment opportunity creates an opportunity cost for waiting. Expected inflation can reduce future purchasing power, and uncertainty can make a promised payment less valuable than an otherwise comparable certain payment. The applicable discount rate should reflect whichever of these considerations belong to the cash flow being valued; they are not universal simultaneous causes, and zero or negative rates can change the ordering.

The time value of money gives us a framework for comparing cash flows that occur at different points in time. Without this framework, how would you choose between receiving $1,000 today versus $1,100 in one year? Or evaluate a business that requires $1 million upfront but promises $200,000 annually for the next seven years? TVM provides the mathematical machinery to answer these questions rigorously.

Interest rates are the mechanism that links present and future values. They quantify the "price" of borrowing money or the "reward" for lending it. In quantitative finance, discount rates are central to debt securities, discounted-cash-flow valuations, and interest-rate-sensitive derivatives. Understanding how rates work, how they compound, and how they are quoted across markets is knowledge that we will use throughout this book.