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 $\text{\textdollar}342857.14$.