Present Value of Annuity Formula

Formula

PV = Pmt x (1 - 1 / (1 + i)n) / i
Variables used in the annuity formula
PV = Present Value
Pmt = Periodic payment
i = Discount rate
n = Number of periods

Use

The present value of annuity formula shows the value today of series of regular payments. The payments are made at the end of each period for n periods, and a discount rate i is applied.

The annuity calculation formula discounts the value of each payment back to its value at the start of period 1 (present value).

Excel Function

The Excel PV function can be used instead of the present value of annuity formula, and has the syntax shown below.

PV(i, n, pmt, FV, type)

*The FV and type arguments are not used when using the Excel present value of an annuity function.

Present Value of Annuity Formula Example

If a payment of 5,000 is received at the end of each period for 10 periods, and the discount rate is 4%, then the value of the payments today is given by the present value of annuity formula as follows:

PV = Pmt x (1 - 1 / (1 + i)n) / i
PV = 5,000 x (1 - 1 / (1 + 4%)10) / 4%
PV = 40,554.48

The same answer can be obtained using the Excel PV function as follows:

PV = PV(i, n, pmt)
PV = PV(4%,10,-5000)
PV = 40,554.48

The present value of annuity formula is one of many annuity formulas used in time value of money calculations, discover another at the link below.

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