# Present Value of a Perpetuity Calculator

Instructions: Use this Perpetuity Calculator to compute the present value ($$PV$$) of a perpetuity by indicating the yearly payment ($$D$$), the interest rate ($$r$$), and the payment received right now ($$D_0$$), if any (leave empty otherwise): Yearly Payment $$(D)$$ = Interest Rate $$(r)$$ = Amount paid now (if any, leave blank otherwise) $$(D_0)$$ =

## Present Value of a Perpetuity Calculator

More about the this perpetuity calculator so you can better understand how to use this solver

### How do you compute the present value of a perpetuity?

The present value ($$PV$$) of a perpetuity payment $$D$$ depends on the interest rate $$r$$ 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 perpetuity, and its present value ($$PV$$) can be computed using the following formula:

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

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

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

Notice that the above formula does not apply if there a growth in the payment. In that case, you to use a specific perpetuity formula with growth.

If you are trying to compute the present value of a perpetuity in which the yearly payment increases, use the following calculator of growing perpetuities . For payments with infinite number of payments, you can use this present value of perpetuity calculator . ### Example

Question: Find the present value of a perpetuity, which pays out \$12,000 every year, at the end of the year, if the discount rate is 3.5%.

Solution:

This is the information we have been provided with:

• The yearly payment is $$D = 12000$$, the yearly interest rate is $$r = 0.035$$.

Hence, the present value of the annuity is calculated using the following formula:

$\begin{array}{ccl} PV & = & \displaystyle \sum_{n = 1}^{\infty} {\frac{D}{(1+r)^n}} \\\\ \\\\ & = & \displaystyle \frac{D}{1+r} + \frac{D}{(1+r)^2 } + ... \\\\ \\\\ & = & \displaystyle \frac{D}{r} \\\\ \\\\ & = & \displaystyle \frac{12000}{0.035} \\\\ \\\\ & = & 342857.14 \end{array}$

Therefore, we get that the present value for this annuity type is $$\text{\textdollar}342857.14$$.