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What is a Perpetuity? - Definition & Formula

What is a Perpetuity? - Definition & Formula
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  • 0:03 Definition of Perpetuity
  • 0:44 Examples of Perpetuity
  • 2:27 Calculating Perpetuity
  • 3:48 Lesson Summary
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Lesson Transcript
Instructor: Lucinda Stanley

Lucinda has taught business and information technology and has a PhD in Education.

This lesson defines and explains what a perpetuity is. It also provides examples of perpetuities and introduces a formula to calculate the present value of a perpetuity.

Definition of Perpetuity

I will love you in perpetuity.

Just what everyone wants to hear because that means you will be loved forever, until the end of time. Okay, so we don't generally hear anyone say that, but now you have an idea of something being true or lasting forever. Let's talk about how perpetuity works in the financial world.

In the financial world, perpetuity refers to payments that are made without an end or maturity date. A perpetuity is classified as an annuity, which is something that earns a dividend or receives a payment at a regularly scheduled interval, generally yearly. So, how exactly does that work? Let's take a look at some examples to give you an idea.

Examples of Perpetuity

Many corporations and governments issue bonds to investors because they need to have an influx of cash to accomplish a goal, such as building a new facility or, in the case of a municipal government, to build a new school. They sell the bond to get the cash they need and agree to pay the investor a set interest payment, or dividend, over the life of the bond with the intention of paying on the amount borrowed at the end of its maturity. If they don't want to set a maturity date, or a date when they will have to pay the principal amount of the bond, they can create a perpetual bond. This is a bond without a maturity date so that the issuing entity does not have to repay the principal (although they can buy the bond back), but does have to pay the yearly interest for as long as the bond exists.

One common example of a perpetual bond is a consol, which is issued by the British government. People who hold that bond will receive interest payments forever. If they sell the bond, the next purchaser will receive the interest payment until they sell it or bequeath it to their heirs. Unlike other types of bonds, the consol does not have a maturity date, so as long as it is out there, it will pay interest to whomever owns it - forever.

Another type of perpetuity you might encounter are estates, or property that is held in a trust, so the recipients of the trust will receive money back from the estate (or property) forever. For example, say your great aunt Bertha has a sizable fortune, and she wants you to receive payments from that fortune all your life. She can put the fortune into a trust, and the interest from that trust is paid to you every year for the rest of your life. When you die, you can designate one of your children to receive the interest payment from the trust; this goes on in perpetuity.

Calculating Perpetuity

How do we know what a perpetuity is worth? That can actually get a little complicated; because a perpetuity doesn't have a maturity, it potentially can earn money forever. However, because of inflation, the money it earns in the future will be worth less than the money it earns today, so as time goes on, value will decrease and be discounted.

So how do you calculate the value of a bond or asset held in perpetuity?

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