For many investment decisions, it is necessary to find the principal, or present value, that corresponds to a given future value.

Example 4.4.1

Consider a note that will pay $10,000 to whoever owns it three years from now. If an investor wants to earn 10% compounded annually, what is the most he or she should pay for the note?

You have:

• i=10%=0.10 per year
• n=3 years
• FV= $10,000

Thus, using the compound-interest formula:

$\begin{align*} &PV(1+i)^n=FV\\ &PV(1.10)^3=$10,000\\ &PV=\frac{$10,000}{1.1^3} =$7,513.15\\ \end{align*}$

This result can be checked by accumulating the money in an account, as shown in the next box.

Formula for Present Value