REVERSION. By a reversion, in the widest sense, is meant n right of property the enjoyment of which is to commence at some future mood, fixed or depending on contingencies, and is to continue either for ever or during a term either fixed or depending on a contingency : anything in fact which is to be entered ou, or which may be entered on, at a future time, is a reversion in books which treat on the value of property. Tho legal sense of the word is more restricted.
Thus an assurance of 100L, or a contract to pay 1001. at the death of a given individual, is ION. In reversion to the executors of that individual. Our object in this article is to treat of this most common species of reversionary contract, life insurance or assurance.
The value of a reversion depends in a very easy manner upon the value of the corresponding annuity; that is, any given sum, say 100t, to be received Owe a given event arrives, depends for its value upon that of 100/. a-year to be received till the event arrives. Suppose, for example, that money makes five per cent., and that an annuity, say upon a life, is worth fourteen years' purchase, upon the method of calculation explained in Aosrorre. That is, 100/. paid a year hence, and again two years hence, and so on as long as the life lasts, is now worth 1400/. Required the value of 1001. to be paid at the end of the sier* in which the life drops. We must now reason as follows : Suppose a perpetual annuity of 100/. a-year is to be enjoyed by A during his life, and.by his legatees after him. By hypothesis A's por tion is now worth 1400/., and ( money making five per cent.) the annuity for ever is worth 20 years' purchase, or consequently the legatees' interest is now worth 2000-1400, or 600/, But at the end of the year of death the legatee will come into 1001. current payment, and a perpetual annuity worth 2000/.; for the re mainder of a perpetual annuity is also a perpetual annuity : his interest will then be worth 21001. Thence we have ascertained that 2100/. at the end of the year of death is now worth 600/. ; and the rule of three then gives the value of any other sum : thus 100/. at the end of the year of death is now worth V., or 28/. Ils. 5Id. Hence the following easy Rutr..—To find the value of a given reversion, subtract the value of the same annuity from that of a perpetual annuity, and divide the difference by one more than the number of years' purchase in a per petual annuity : or multiply the excess of the number of years' purchase in a perpetual annuity of H. over that in the life annuity by
the reversionary sum, and divide as before.
Next, to find what premium should be paid for the reversion. A premium differs from an annuity in that a sum is paid down, and also at the end of eve*. year : consequently it is worth one year's purchase more than an annuity. In the preceding question, the annuity was worth 14 years' purchase; consequently the premium now is worth 15 years purchase. But the present value of all the premiums is to be also the present value of the reversion, or 281. lls. 5:d., whence the premium should be the 15th part of this, or 11. 18s. Id. Hence to find the premium, divide the present value of the reversion by one more than the number of years purchase in the life annuity. But when, as most commonly happens, the premium is wanted without the present value, the following is an easier Rom—Divide the reversionary sum separately by one more than the number of years' purchase in the perpetual annuity, and ono more than the number of years' purchase in the life annuity : the difference of the quotients is the premium required. Thus if in the preceding example we divide 100/. by 20+1 and by 14+1, or by 21 and 15, we find 4/. Ms. 3d. and (3/. 13s. 4d., which differ by 1!. 18s. M., the same as before.
Tho life we have been tacitly considering, when we talked of an annuity being worth 14 years' purchase at five per cent., is one of about 36 years of age. The first impression must be, that the pro posed premium is ridiculously small. Make it up to .2/., and it will be 50 years before the premiums reach 100/. Some such considera tion must have moved the law officers of the crown, in 1760, when they refused a charter to the Equitable Society, then charging a pre mium of about 4!. at the age of 36, on account of the lowness of their terms. But it is to be remembered that those who receive the premiums are to invest them immediately at five per cent., and are to invest the interest, thus making compound interest ; persons aged 36 live, one with another, about 30 years, which is sufficient tune for the premiums, with their interest, to realize 100/. for each person, one with another.