# Present Value Annuity Tables

The purpose of the present value annuity tables is to make it possible to carry out annuity calculations without the use of a financial calculator.

They provide the value now of 1 received at the end of each period for n periods at a discount rate of i%.

The present value of an annuity formula is:

`PV = Pmt x (1 - 1 / (1 + i)n) / i`

As can be seen present value annuity tables can be used to provide a solution for the part of the present value of an annuity formula shown in red. Additionally this is sometimes referred to as the present value annuity factor.

`PV = Pmt x Present value annuity factor`

## Present Value Annuity Table Example

As an illustration of the use of the tables we can calculate the present value of 5,000 received at the end of each year for 12 years, if the discount rate is 7%?

```Pmt = 5,000
n = 12
i = 7%
PV = Pmt x (1 - 1 / (1 + i)n) / i
PV = 5,000 x (1 - 1 / (1 + 7%)12) / 7%
PV = 5,000 x Present value of annuity factor for n = 12, i = 7%
PV = 5,000 x 7.9427
PV = 39,713.50```

It is important to realize that the present value annuity factor of 7.9427 is found using the tables below as follows. Values referred to are highlighted in yellow.

1. Starting at the left hand side. Find the number of periods n. In this case 12.
2. Follow along this row until you reach the column representing the discount rate. In this example 7%
3. Note the present value annuity factor. In this example 7.9427.