Calculator of the Present Value of a Growing Perpetuity

More about the this growing perpetuity calculator so you can better understand how to use this solver: The present value ($PV$) of a growing perpetuity payment $D$ depends on the interest rate $r$, the growth rate $g$ and whether or not the first payment is right now or at the end of the year.

How do you compute a growing perpetuity

If the first payment of a perpetual stream of payments of $D$ is made at the end of the year, we then have a regular growing perpetuity, and its present value ($PV$) can be computed using the following growing perpetuity formula :

$$PV = \displaystyle \sum_{n = 1}^{\infty} \frac{D \times (1+g)^{n-1}}{(1+r)^n} = \frac{D}{r-g}$$

The derivation of the perpetuity formula is related with the calculation of a geometric series with a ratio that has an absolute value that is less than 1, which holds in this case.

On the other hand, if the first payment $D_0$ is made now, then we have a growing perpetuity due, and its present value ($PV$) can be computed using the following formula.

$$PV = D_0 + \displaystyle \sum_{n = 1}^{\infty} \frac{D \times (1+g)^{n-1}}{(1+r)^n} = D_0 + \frac{D}{r-g}$$

Related Finance Calculators

If you are trying to compute the present value of a perpetuity in which the yearly payment remains constant, use the following calculator of a regular perpetuity , or simply use $g = 0$.

Now, if what you need is a cash flow that does not come at perpetuity, and instead has a finite number of years associated to it, you can use this present value of an annuity calculator.