# Present Value (PV) Calculator

### What is Present Value (PV)?

Present Value (PV) is the current value of future money.

It is today’s value of a future lump sum or future series of payments. It calculates today’s value of future money using an interest rate and number of time periods.

### 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:

$latex \text{Present Value} = \frac{\text{Future Value}}{(1 +\text{Rate of Return})^\text{Periods}}$

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

For a payment annuity that occurs at the beginning of each period (present value of an annuity due), the formula is:
$latex \text{Present Value} = \text{Payment} \times (\frac{(1 + \text{Rate of Return})^\text{Periods} – 1}{\text{Rate of Return}}) \times (1 + \text{Rate of Return})$

### 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.