What is Perpetuity?

Legal Definition
A perpetuity is an annuity that has no end, or a stream of cash payments that continues forever. There are few actual perpetuities in existence (the United Kingdom (UK) government has issued them in the past; these are known and still trade as consols). Real estate and preferred stock are among some types of investments that affect the results of a perpetuity, and prices can be established using techniques for valuing a perpetuity. Perpetuities are but one of the time value of money methods for valuing financial assets. Perpetuities are a form of ordinary annuities.

The concept is closely linked to terminal value and terminal growth rate in valuation.
-- Wikipedia
Legal Definition
Estates. Any limitation tending to take the subject of it out of commerce for a longer period than a life or lives in being, and twenty-one years beyond; and in case of a posthumous child, a few months more, allowing for the term of gestation; Randell on Perpetuities, 48; or it is such a limitation of property as renders it unalienable beyond the period allowed by law. Gilbert on Uses, by Sugden, 260, note.

2. Mr. Justice Powell, in Scattergood v. Edge, 12 Mod. 278, distinguished perpetuities into two sorts, absolute and qualified; meaning thereby, as it is apprehended, a distinction between a plain, direct and palpable perpetuity, and the case where an estate is limited on a contingency, which might happen within a reasonable compass of time, but where the estate nevertheless, from the nature of the limitation, might be kept out of commerce longer than was thought agreeable to the policy of the common law. But this distinction would not now lead to a better understanding or explanation of the subject; for whether an estate be so limited that it cannot take effect, until a period too much protracted, or whether on a contingency which may happen within a moderate compass of time, it equally falls within the line of perpetuity and the limitation is therefore void; for it is not sufficient that an estate may vest within the time allowed, but the rule requires that it must. Randell on Perp. 49. Vide Cruise, Dig. tit. 32, c. 23; 1 Supp. to Ves. Jr. 406; 2 Ves. Jr. 357; 3 Saund. 388 h. note; Com. Dig. Chancery, 4 G 1; 3 Chan. Cas. 1; 2 Bouv. Inst. n. 1890.
-- Bouviers Law Dictionary
Legal Definition
A future limitation, whether executory or by way of remainder, and of either real or personal property, which is not to vest until after the expiration of or will not necessarily vest within the period fixed and prescribed by law for the creation of future estates and interests, and which i not destructible by the persons for the time being entitled to the property subject to the future limitation, except with the concurrence of the individual interested under that limitation. Lewis, Perp. 164; 52 Law Lib. 139 Any limitation tending to take the subject of it out of commerce for a longer period than a life or lives in being, and twenty-one years beyond, and, in case of a posthumous child, a few months more, allowing for the term of gestation. Rand. Perp. 48. Such a limitation of property as readers it unalienable beyond the period allowed by law. Gilb. Uses, (Sugd. Ed.) 260. And see Ould v. Washington Hospital, 95 U. S. 303, 24 L. Ed. 450; Duggan v. Slocum, 92 Fed. 806, 34 C. C. A. 676; Waldo v. Cummings, 45 111. 421; Franklin v. Armfleld, 2 Sneed (Tenn.) 354; Stevens v. Annex Realty Co., 173 Mo. 511, 73 S. W. 505; Griffin v. Graham, 8 N. C. 130, 9 Am. Dec. 619; In re John's Will, 30 Or. 494, 47 Pac. 341, 36 L. R. A. 242.
-- Black's Law Dictionary
Legal Definition
Any limitation or condition which may take away or suspend the absolute power of alienation for a period beyond the continuation of lives in being. See 108 Cal. 627, 49 Am. St. Rep. 97, 41 Pac. 772.
-- Ballentine's Law Dictionary