Present Value (PV) Calculator

LAST UPDATE: April 8th, 2018

What is a Present Value (PV)?

Present value (PV) is a financial calculation used when determining the time value of money to determine the “present day value” of a series of financial inputs.
It takes into consideration a value at a time in the future as well as the interest rate and payments occurring each compounding period.
As this calculator is structured to parallel the results of a financial calculator, inputs and outputs will be similar – for example, a negative present value (or payment) means an outflow as opposed to a directly negative number.

How is the Present Value calculated?

Present value calculates through a financial formula used to determine the time value of money.
There are two separate calculations involved: The base sum as well as the payment schedule.
For the base sum, the formula is:

$\text{Present Value} = \frac{\text{Future Value}}{(1 +\text{Rate of Return})^\text{Periods}}$
For a payment annuity that occurs at the end of each period, the formula is:
$\text{Present Value} = \text{Payment} \times (\frac{1 - (1 + \text{Rate of Return})^(-\text{Periods)}}{\text{Rate of Return}})$
For a payment annuity that occurs at the beginning of each period, the formula is:
$\text{Present Value} = \text{Payment} \times (\frac{(1 + \text{Rate of Return})^\text{Periods} - 1}{\text{Rate of Return}}) \times (1 + \text{Rate of Return})$

What are Payments at start or end of a period?

A payment at the beginning of a period would mean that the payment (or deposit) occurs at the beginning of each period. A payment at the end of a period would mean that the payment (or deposit) occurs at the end of each period.