## Formula

PV = Pmt x (1 + i) x (1 - (1 + g)^{n}x (1 + i)^{-n}) / (i - g)

**Variables used in the annuity formula**

PV = Present Value

Pmt = Periodic payment

i = Discount rate

g = Growth rate

n = Number of periods

## Use

The present value of a growing annuity due formula shows the value today of series of periodic payments which are growing or declining at a constant rate (g) each period. The payments are made at the **start** of each period for n periods, and a discount rate i is applied.

A growing annuity due is sometimes referred to as an increasing annuity due or graduated annuity due.

The formula discounts the value of each payment back to its value at the start of period 1 (present value). When using the formula, the discount rate (i) should be greater than the growth rate (g).

## Present Value of a Growing Annuity Due Formula Example

If a payment of 8,000 is received at the start of period 1 and grows at a rate of 3% for each subsequent period for a total of 10 periods, and the discount rate is 6%, then the value of the payments today is given by the present value of a growing annuity due formula as follows:

PV = Pmt x (1 + i) x (1 - (1 + g)^{n}x (1 + i)^{-n}) / (i - g) PV = 8,000 x (1 + 6%) x (1 - (1 + 3%)^{10}x (1 + 6%)^{-10}) / (6% - 3%) PV = 70,543.46

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