**Perpetuity Definition:**

A perpetuity is an annuity that provides payments indefinitely. Since this type of annuity is unending, its sum or future value cannot be calculated.

**Examples of perpetuity:**

- Local governments set aside monies so that funds will be available on a regular basis for cultural activities.
- A children’s charity club set up a fund designed to provide a flow of regular payments indefinitely to needy children.

Therefore, what happens in a perpetuity is that once the initial fund has been established the payments will flow from the fund indefinitely which implies that these payments are nothing more than annual interest payments.

**How to calculate a perpetuity?**

With perpetuities it is necessary to find a present value based on a series of payments that go on forever.

The formula for calculating the present value of a perpetuity is:

** R****A ∞ = —-**** i**

Where:

R = the interest payment each period

i= the interest rate per payment period

**Example:**

Alan wants to retire and receive $3,000 a month. He wants to pass this monthly payment to future generations after his death. He can earn an interest of 8% compounded annually. How much will he need to set aside to achieve his perpetuity goal?

Solution: R = $3,000

i = 0.08/12 or 0.00667

Substituting these values in the above formula, we get

$3000

A ∞ = ———

0.00667

= $449,775

If he wanted the payments to start today, we must increase the size of the funds to handle the first payment. This is achieved by depositing $452,775 which provides the immediate payment of $3,000 and leaves $449,775 in the fund to provide the future $3,000 payments.