In financial markets, there are many examples of cash flows that occur at some point in the future but which need to be evaluated today. A cash flow in the future has a value today called the present value. Similarly, a cash flow today has a value in the future known as the future value. Present value and future value are determined by the interest rate and the time period elapsed. They are crucial concepts in finance. For example, the price of a bond is the sum of the present value of all the cash flows expected to be generated by the bond in the future, the mark-to-market value of an interest swap is the sum of the present values of all the cash inflows and outflows from the swap in the future, and the value of an option is the present value of the expected payoff of the option at the exercise date.

This tutorial describes the concepts of present value and future value, and the relationship between them. It is essential for understanding the way in which securities and derivatives are priced, and how decisions are made in financial markets.

Objectives
On completion you will be able to:

• Calculate the future value of an investment for a given present value and a given interest rate
• Recognize the relationship between the present value, future value, and discount factor
• Calculate the value of a perpetuity and an annuity
• Use the present value and future value formulas to solve for an unknown rate or number of periods, and distinguish between nominal and real interest rates