LIFE INSURANCE, OR REVER SION. By a reversion, in the widest sense, is meant a right of property the en joyment of which is to commence at some future period, fixed or depending on con tingencies, and is to continue either for ever or during a term either fixed or de pending on a contingency : anything in fact which is to be entered upon, or which may be entered on at a future time, is a reversion in books which treat on the value of property. The legal sense of the word is more restricted.
Thus an assurance of 100/., or a con tract to pay 100/. at the death of a given individual, is 1004 in reversion to the executors of that individual. Our object in this article is to treat of this most com mon 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 1001., to be received when a given event arrives, depends for its value upon that of 100/. a year to be re ceived 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 AN. NUITY, p. 141. 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 100/. to be paid at the end of the year* in which the life drops. We must now reason as fol lows :—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 portion is now worth • Assurance companies usually pay in a few months after proof of death, which gives a trifling advantage to the assured, not worth considering in a very elementary statement of the question.
14001., and (money making five per cent) the annuity for ever is worth twenty years' purchase, or 20001.; consequently, the legatee's interest is now worth 20001. – 1400, or 600/. But at the end of the year of death the legatee will come into 100/. current payment, and a perpetual
annuity worth 20001; for the remainder of a perpetual annuity is also a perpetual annuity : his interest will then be worth 21001. Hence we have ascertained that 21001. at the end of the year of death is now worth 600l.: 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 °fl., or 281. Us. Sid. Hence the following easy RULE.—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 perpe tual annuity 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 every year: consequently it is worth one year's purchase more than an annuity. In the preceding question, the annuity was worth fourteen years' purchase ; consequently the premium now is worth fifteen years' purchase. But the present value of all the premiums Is to be also the present value of the reversion, or 281. 1 Is. 5fd., whence the premium should be the fifteenth part of this, or 11. 18s. ld. 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 RULE.—Divide the reversionary sum separately by one more than the number of years' purchase in the perpetual annu ity, and one 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 ex ample we divide 100/. by 20+1 and by 14+1, or by 21 and 15, we find 41. 15s. 3d. and 61.13s. 4d., which differ by 11. 18s. Id. the same as before.