# Calculator of the Present Value of an Annuity

Instructions: Compute the present value ($$PV$$) of an annuity by indicating the yearly payment ($$D$$), the number of years that the payment will be received for ($$n$$), the interest rate ($$r$$), and the payment that is received right now ($$D_0$$), if any (leave empty otherwise):

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

## Present Value of an Annuity Calculator

More about the this step by step annuity calculator so you can better understand how to use this solver: The present value ($$PV$$) of an annuity payment $$D$$ depends on the interest rate $$r$$, the number of years the payment will be received from, and whether or not the first payment is right now or at the end of the year. If the first payment of an annuity stream of payments of $$D$$ is made at the end of the year, we then have a regular annuity, and its present value ($$PV$$) can be computed using the following formula:

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

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

$PV = D_0 + \displaystyle \sum_{k = 1}^{n} \frac{D}{(1+r)^k} = D \left(\frac{1}{r} - \frac{1}{r(1+r)^n} \right)$

If you are trying to compute the present value of an annuity in which the yearly payment increases, use the following calculator of growing annuities.

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