## 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:

- future value = $5,000
- interest rate = 5%
- number of periods = 6

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__