Present Value Example

Prepared by Pamela Peterson

Problem

Suppose you are depositing an amount today in an account that earns 5% interest, compounded annually. If your goal is to have $5,000 in the account at the end of six years, how much must you deposit in the account today?

Solution

The following information is given:

We want to solve for the present value.

present value = future value / (1 + interest rate)number of periods

or, using notation

PV = FV/ (1 + r)t

Inserting the known information,

PV = $5,000 / (1 + 0.05)6

PV = $5,000 / (1.3401)

PV = $3,731

We can use the present value table (or table of discount factors) to solve for the present value.

PV = FV (discount factor for r and t)

The discount factor, from the table, is 0.7462. Therefore,

PV = $5,000 (0.7462)

PV = $3,731