Perpetuities – Definition & Calculation

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.



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