# Present Value (PV) of an annuity due calculator

### What is a Present Value (PV) of an annuity due?

Present value (PV) of an annuity is a financial calculation used when determining the “today” value of an set of annuity payments that occur each compounding period, when the payments occur at the beginning of the compounding period (as opposed to a regular annuity, where the payments occur at the end of the 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 of an Annuity Due calculated?

The PV of an annuity due is calculated through a financial formula used with the time value of money.
$text{Present Value} = (frac{text{Annuity Payment}}{Interest Rate}) times (1 - frac{1}{(1 + text{Interest Rate})^text{Number of Periods}}) times (1 + text{Interest Rate})$

### Example

We will receive \$100 each year for the next 12 years. The interest rate at the moment is 2.2% compounded annually. What is the present value of this annuity?
$text{Present Value} = (frac{-100}{0.022}) times (1 - frac{1}{(1 + 0.022)^12}) times (1 + 0.022)$
$text{Present Value} = (-4545.45454545) times (1 - frac{1}{(1.022)^12}) times (1.022)$
$text{Present Value} = (-4545.45454545) times (1 - frac{1}{1.29840671}) times (1.022)$
$text{Present Value} = (-4545.45454545) times (1 - 0.77017470) times (1.022)$
$text{Present Value} = (-4545.45454545) times 0.2298253 times (1.022)$
$text{Present Value} = -1067.64$

### What are periods?

Periods are the number of times that compounding (and payments) take place.

### What is the rate?

The rate is the amount of interest earned per compounding period.

### What is Payment (PMT)?

A payment is an amount either deposited or withdrawn at each compounding period. A negative number designates an amount that is deposited, while a positive one withdrawn. For example, if \$100 is deposited each compounding period, it would be entered as '-100', while if \$75 was payed out each compounding period, it would be entered as '75'.