# Calculator of the Present Value of a Growing Annuity

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):

Yearly Payment $$(D)$$ =
Interest Rate $$(r)$$ =
Growing Rate $$(g)$$ =
Amount paid now (if any, leave blank otherwise) $$(D_0)$$ =
Number of Years $$(n)$$ =

## 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:

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

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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