PV = Pmt x (1 + i) x (1 - 1 / (1 + i)n) / i
PV = Present Value
Pmt = Periodic payment
i = Discount rate
n = Number of periods
The present value of annuity due formula shows the value today of series of regular payments. The payments are made at the start of each period for n periods, and a discount rate i is applied.
The formula discounts the value of each payment back to its value at the start of period 1 (present value).
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 argument is not used when using the Excel present value of an annuity due function.
Example Using the Present Value of Annuity Due Formula
If a payment of 6,000 is received at the start of each period for 9 periods, and the discount rate is 6%, then the value of the payments today is given by the present value of annuity due formula as follows:
PV = Pmt x (1 + i) x (1 - 1 / (1 + i)n) / i PV = 6,000 x (1 + 6%) x (1 - 1 / (1 + 6%)9) / 6% PV = 43,258.76
The same answer can be obtained using the Excel PV function as follows:
PV = PV(i, n, pmt,,1) PV = PV(6%,9,-6000,,1) PV = 43,258.76
The present value of annuity due formula is one of many annuity formulas used in time value of money calculations, discover another at the link below.