## Formula

PV = Pmt / (i - g)

**Variables used in the annuity formula**

PV = Present Value

Pmt = Periodic payment

i = Discount rate

g = Growth rate

## Use

The present value of growing perpetuity 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 end of each period, continue forever, and have a discount rate i is applied.

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

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) must be greater than the growth rate (g).

## Present Value of a Growing Perpetuity Formula Example

If a payment of 6,000 is received at the end of period 1 and grows at a rate of 3% for each subsequent period and continues forever, and the discount rate is 6%, then the value of the payments today is given by the present value of a growing perpetuity formula as follows:

PV = Pmt / (i - g) PV = 6,000 / (6% - 3%) PV = 200,000

The present value of a growing perpetuity formula is one of many used in time value of money calculations, discover another at the links below.