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.