An annuity can be a perpetuity, depending on how it is set up. An annuity is an investment that makes regular payments throughout the year. A perpetuity is a type of annuity that is set up so that the payments never end. As long as an investor owns a perpetuity, he will keep receiving payments. When the investor dies, the perpetuity will pass on to his heirs and keep making payments as normal. If the investor sells the perpetuity, the new owner will receive the payments.
Most annuities eventually stop making payments. They might stop making payments after a set number of years or after the contract owner dies. However, if an annuity is set up so that it never stops making payments, then it is a perpetuity. In other words, all perpetuities are annuities, but not all annuities are perpetuities.
Because of their extremely long, potentially infinite time frame, perpetuities are relatively rare investments. Annuity companies don't sell perpetuities. The closest example of a true perpetuity is a type of bond from the British government known as a consol. These bonds have no maturity date and keep making interest payments forever – or at least as long as the British government is in existence.
Preferred stock in companies can also resemble perpetuities. Some preferred stock is sold without an expiration date. These stocks pay out a fixed dividend rate out of the company's profits. This structure resembles a perpetuity; as long as the company is in business and making a profit, the preferred stock will pay out its set payments.