**Present value annuity factor = [1 – (1 + r)**^{-n}**] ÷ r**

r = rate for theperiod

n = number of periods

The present value annuity factor is utilized to calculatethe PV of cash flows from investment to be received in the future. The approachor principle behind this formula is to first determine the discount rate andthen use it to calculate the PV of an investment. As the discount rate goes toupper side the present value of annuity goes to the downside. This discountrate is also known as the present value annuity factor.

The formula is based on the concept of the time value of money. It is basically the idea that a specific amount available today will worth more than the same amount available after 2 years. The underlying concept for that is inflation because prices changes over time and thus the currency devalues over time. For example, if $500 is received today it will worth more than $500 received after 2 years.

The time value of money leads to the concept of **Present value.** Suppose that if a personhas two options to receive an amount of $500 today vs. $570 after 5 years. Thento make a precise decision and make more profits he/she must have to calculatethe value of $570 received after 5 years at the present time. This is where thepresent value annuity factor comes in.

## How present value annuity factor is useful

Present value annuity factor intends to make the calculationprocess simple and quick. A complete Annuity Table is available where anumber of values are available for different terms and rates. From this table,one has to first find the respective discount factor (annuity factor) on thebasis of the number of periods and rate per period. To get the final amount(present value of an annuity) we then multiply the per dollar amount with thatfactor.

### Present value annuity factor example

Suppose that an individual is seeking to calculate thepresent value of perpetuity where annually he has to pay $800 for up to 6 yearsat a rate of 6%. We found the annuity factor (4.9173) for 6-years @6% rate. So,now we can multiply the payment with annuity factor to give;

Present value of investment = 4.9173 × 800

PV of investment = $3933.84

### How the present value annuity factor formula is derived?

The PV annuity factor is basically separated from the presentvalue annuity formula which is as follows;

Present value annuity formula = P [{1 – (1 + r)^{-n}}÷ r]

If we take out the variable from the above formula then wecan get the annuity factor as a left over. The formula at the top is derived byusing the same approach.