The Time Value of Money (TVM)

A dollar today is worth more than a dollar tomorrow. This simple observation is the foundation of almost all quantitative finance. Why? Because you can invest that dollar today and earn interest.

1. Compounding and Future Value (FV)

When you invest money, you earn interest not only on your initial principal but also on the interest previously earned. This is called Compounding.

$FV = PV \times (1 + r)^n$

2. Discounting and Present Value (PV)

Discounting is the reverse of compounding. It helps us determine what a future payment is worth in today’s terms.

$PV = \frac{FV}{(1 + r)^n}$

3. Net Present Value (NPV)

In financial engineering, we use NPV to decide if a project or investment is worth pursuing. We sum up all future cash inflows and outflows, discounted to the present.

💡 Professor’s Tip

The discount rate ($r$) is the “Price of Time.” It reflects not just the risk-free interest rate, but also the risk premium of the specific investment. Choosing the right discount rate is more of an art than a science.

🔗 Next Step

• Ch3: Basics of Derivatives