Annuity present value is the current worth of a series of equal payments to be received or paid in the future. This concept applies the time value of money to determine how much a stream of future payments is worth today, given a specified rate of return.

Ordinary Annuity (End of Period)An ordinary annuity assumes payments occur at the end of each period. Its present value is calculated using the formula:

$$PV = PMT \times \left[ \frac{1 - (1 + r)^{-n}}{r} \right]$$

Annuity Due (Beginning of Period)An annuity due assumes payments occur at the beginning of each period. Its present value is calculated by adjusting the ordinary annuity formula:

$$PV = PMT \times \left[ \frac{1 - (1 + r)^{-n}}{r} \right] \times (1 + r)$$

Present Value Annuity Factor (PVAF)The Present Value Annuity Factor (PVAF) is a multiplier used to calculate the present value of an annuity. It represents the present value of $1 paid/received for n periods at interest rate r:

$$PVAF_{r,n} = \frac{1 - (1 + r)^{-n}}{r}$$

Where r is the interest rate per period and n is the number of periods. Once calculated, you can multiply this factor by the payment amount to find the annuity's present value.