Let’s represent the value of $1 to be received two years from now as X_2yrs. If you lend out X_2yrs today for two years, you will receive:

which you then reinvest to receive:

From Equation 9A-5 we can calculate how much you would have to lend today in order to receive $1 two years from now:

To solve for X_2yrs, divide both sides of Equation 9A-6 by (1 + r)² to arrive at:

For example, if r = 0.10, then X_2yrs = $1/(1.10)² = $1/1.21 = $0.83.

Equation 9A-7 points the way toward the general expression for present value, where $1 is paid after N years. It is

In other words, the present value of $1 to be received N years from now is equal to $1/(1 + r)^N.