LIF
From the value of the fee fimple or perpetuity, fubtradt the value of the life in pofleffion ; what remains will be the value of the reverfion.
Thus fuppofing that A is 60 years of age ; an annuity upon hk life, intereft at 5 per Cent, would be 8. 39; which bein^ fubtracted from the value of the fee, or perpetuity 20, the remainder will be 11. 61 ; which is the prefcnt value of the expectation of B.
By this rule the value of an eftate fubjecl to a jainture may be determined.
In like manner, fuppofing that C were to have an annuity for him and his heirs for ever, after the lives of A and B, then from the perpetuity or fee fimple fubtracfing the value of the longeft of the two lives A and B, the remainder will exprefs the value of C's expectation.
Thus, fuppofing the ages of A to be 40, and of B to be 50, the value of an annuity upon the longer! of thefe two livts would be found by the foregoing rule to be 14. 56 : and this being fubtrafted from the perpetuity 20, the remainder is 5. 44 ; which is the value of C's expectation. V. To find the value of an annuity for lift, after another an- nuity for life.
Suppofe for inftance, that A is in pofleffion of an annuity for his lift, and that B, after the life of A, is to have the annuity &r his lift only, and that his heir or reprefentative is to have nothing, in cafe A furvives B ; what is the value of the life of B, after the life of A.
From the prefent value of the life of B, fubtraift the prefcnt value of the joint lives of B and A, and the remainder will be the value of B's expeclation.
There are many other ufeful queftions, the determinations of which depend on the values of annuities for lives, joint lives, and fucceffive lives ; but it would lead us too far to infert them here : We mult therefore refer the reader to M. De Moivre's annuities on lives ; efpecialfy the fourth edition, which is more correct, than the former. See alfo the Docf rine of Chances, page 211, 212, &c.
We think it proper to add, that Mr. Kerfeboom's Table of the value of annuities for life, does not agree entirely with thofe of M. De Moivre, either at 3, or 3 £ per Cent, intereft. But as Mr. Kerfeboom feems to have taken great pains in his obfervations on the probabilities of life, it may be worth while here to infert his Table.
Mr. Kerfeboom's table of annuities for life.
Let the annuity be 100 guilders a year upon a life under a year old.
Guilds. Its prefent value is ----- 1667 that is 6 per Ct.
■ - 5- 35
■ " 5-45
- 5. 6 S
- 6. 00
3° 60
L I G
Upon a lift of 5 years to 1 inclufive, is 18
IS
20
25 3° 3!
40
45 50 55 60
65
6
- 1835
11
- 1770
16 -
- 1667
21
- 1587
26 -
- i5'5
3i ■
- 1429
36 ■
- 1334
41
- 1212
46
- J°93
5' "
- 971
56 ■
- 840
61 -
- 709
66 ■
- 57°
- 6.
- 7. 00
- 7- 5°
- 8. 25
- 9- 15
- 10. 30
- 11. 40
- 14. 10
- *7- 55
See Phil. Tranf. N° 450. Se<3. 15.
Monfieur de Parcieux has alfo given us many ufeful obferva- tions tending to determine the probability of the duration of the life of man. See Eflai fur les probabilites de la duree de la vie humaine, Paris, 1746. 4to.
According to this gentleman's eftimate, the values of annui- ties for life are higher than thofe of M. De Moivre's Tables. Thus fuppofing intereft at 5 per Cent. Mr. De Parcieux efti- mates an annuity for life of 100 livres, according to the fol- lowing table.
Table of the values of an annuity of 100 livres for life, according to Monfieur de Parcieux. Intereft at 5 per Cent.
3
4 5 6
7 8
9 10
»3
Livres
Age
Livres
Age
1557
'4
1602
2 5
1582
15
J 594
26
1600
i5
1586
-7
1613
'7
1578
28
1620
18
157'
29
1624
•9
1565
30
1627
20
1558
3'
1625
21
'55 1
132
1622
22
1544
1 33
1617
23
■537
134
1610
24
1530
!35
1523
1516
1508
1500
1492 1484
■475 1464
'453
1442
M3I
36 37 38 39
40
41 42 43 44 45 46
47 48
49 5° 51 52 53 54 55 Complement of Li
Livres
Age
1419
56
1407
57 ■
'394
58
■379
59
1362
60
'344
61
r 3 2 4
62
■3°4
63
1284
64
1264
65
1243
66
1222
67
1201
68
1180
69
1 158
70
1136
7i
11 14
72
1091
73
1068
74
104s
75
1022 999 975 950 924 898 871
843 814
784 75 2 722
6 93 604 636 610 584 558 532 506
480 455 431 408 386 3 e 5 345 324 301 278 256
234 210 184 158 132 105 7 1 47
APPEND.
ufed by Mr. De Moivre, for that time which remains from a given age to the ex:remity of old age, eftimated by that author at 86 years. Annuit. on Lives, p. 14. Doflnne of Chances, p. 213 feq Thus, fuppofing an age of 50, the Complement tf life will be 36 ; becaule this number is the difference between 86 and 50.
Expeclation of Life, is ufed by Mr. De Moivre, for the time which a peifon of a given age may ju% exped to continue in being, that is when the chance for his living or dyifig be- comes equal. ° * ° According to that gentleman's calculation, upon the fuppo- frtionof an equal decrement of life, the Elation of life would be exprefled by | w , if „ denotes the complement of hfe. Thus the expeclation of life for a man. of 50 years of age will be, 18=--: That is, he had an equal chance, or of 1 to 1, of living 18 years. But if that interval be once attain- ed, there anfes a new expeaation of | k; and afterwards of £ n, &c. Annuities p. 65, 66,
Hence he gives the folution of the following problem : To find the expeclation of two joint -lives, that is; the time which two lives may expecT; to continue together in being- . . n
For this the rule is, from one half of the fhortefl complement fubtraa the fixth part of its fquare, divided by the greateft complement, the remainder will exprefs the number 0? years fought. *
Thus fuppofing a life of 40, and another of 50 ; the fhortefl: complement will be 36 ; the greateft 46' ; § of the fhorteft will be 18 ; the fquare of 36 is 1296, whereof the fixth part is 216, which being divided by 46, the quotient will be ^ = 4. 69 ; and this being footr acted from 18, the remainder 13. 31 will exprefs the number of years due to the two joint lives. As to the probability of one Life's fur-viving others, fee de Moivre, Annuit. p. 54. Doct. of Chances, p. 223.
Infurance upon Lives. The value of infttrances upon Lives depends upon the probability of the continuance of any pro- pored life or lives, during any propofed term. Any queftions of this kind may be determined from Dr. Halley's Tabled arid from the principles of the Doctrine of Chances. But, as far as we can learn of the practice on fucti occafions, the premi- ums paid to infurers are generally higher than any computation founded on obfervations concerning the probabilities of human life', will warrant. Thus it is not unufual to make a perfon pay 5 per Cent, for the infurance of his life for a twelve- month, that is, in cafe the perfon dies within the year, the infurer is to pay loo /. for every 5 /. received. Now it ap- pears from Dr. Halley's Tabic, which efti mates the probability or life low enough, that 5 per Cent, is an adequate value only for a life or an advane'd age, fuch as 64.
Life everlafling, a name by which the Elicbryfum, or Gna~ pbalittm, of botanical writers, is fometimes called. See the article Gnaphalium, Suppl.
LIGHT (Cycl.) — The motion of Light was deduced from the obfervations of an apparent inequality in the times of the eclip- fes of the fatellites or Jupiter, by Mr. Romer * ; but the con- clufion was attacked by Monfieur Caffini; "Mr. Romer's opi- nion found an able advocate inDr.Halley b ; who removedCaffi- ni's difficulty, and left Mr. Romer's conclufion in itsfull force. In the year 1707, Monfieur Maraldi endeavour'd to give a new ftrength to Caffini's arguments ; but Monfieur Romer's doctrine found a new defender in Mr. Pound c . — [a See Phil. Tranf. N° 136. Lowthorp's Abridg. Vol.1, p. 409. b Phil. Tranf abr. by Lowth. Vol. I. p. 409, 422. c *sGrav. Phyr. Elem. N° 2636, feqq.] Mr. Romer's deduction from his theory was, that Light fpent about eleven minutes in its paflage from the fun to us ; but it hath fince been concluded by others, from the like eclipfes of Jupiter's fatellites, that it is propagated as far irta- bout feven minutes. — [ b Phil. Tranf. N° 406, 'sGravef* andcy Phyr. Elem. N 2638.]
2D Our
