**Instructions:** Compute the present value (\(PV\)) of a growing annuity by indicating the yearly payment (\(D\)), the interest rate (\(r\)), the number of years (\(n\)), the growth rate (\(g\)) and the payment received right now (\(D_0\)), if any (leave empty otherwise):

#### Calculator of the Present Value of a Growing Annuity

More about the *this growing annuity calculator* so you can better understand how to use this solver: The present value (\(PV\)) of a growing annuity payment \(D\) depends on the interest rate \(r\), the growth rate \(g\), the number of years the payment is received for \(n\), and whether or not the first payment is right now or at the end of the year. 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 annuity, and its present value (\(PV\)) can be computed using the following formula:

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

\[ PV = D_0 + \displaystyle \sum_{k = 1}^{n} \frac{D \times (1+g)^{k-1}}{(1+r)^k} = \frac{D}{r-g}\left( 1 - \left( \frac{1+g}{1+r} \right)^n \right)\]If you are trying to compute the present value of an annuity in which the yearly payment remains constant, use the following calculator of a regular annuity, or simply use \(g = 0\).

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