Annuity implies a sum of money payable yearly, half-yearly, or quarterly, to continue for a certain number of years, for life, or for ever.

An annuity is called an arrear, when it continues unpaid after it becomes due; and is said to be in reversion, when the purchaser, upon paying the price, does riot immediately enter upon possession: the annuity not commencing till some time after.

The interest upon annuities may be computed either in the simple or compound manner. But the latter, being most equitable, is ge-nerally preferred.

In the first class, viz. in those which extend for a limitted period, the principal considerations are, the annuity, rate, and time being given, to find the amount, or sum of yearly payments, and interest. These are readily ascertained, by a series of algebraical calculations.

In freehold estates, the principal circumstances to-be attended to, are,

1. The annuity, or yearly rent.

2. The price, or present value ; and,

3. The rate of interest.

The value of life-annuities is determined by comparative observations and calculations derived from, the bills of mortality. Several computations have been made for this purpose; the most esteemed of which are those by Dr. Hal-LEY, Mr. Simpson, and M. De MOIVRE.

Breslaw, the capital of Silesia, being a central place, and not much crowded, was fixed upon by Dr. Halley, who had recourse to the bills of mortality, when he composed his table. He selected l000 persons, all born in one year, and observed, how many of these remained alive every year from their birth, to the extinction of the last ; and, consequently, ascertained the; number which died in each year, as follows:

Agep>

1

Persons living.

Age. 24

Persons living.

Age. 47

Persons living;.

Age.

70

Persons living.

1000

573

377

142

2

855

25

567

48

367

71

131

3

798

26

560

40

357

72

120

4

760

27

553

50

346

73

1O9

5

732

28

546

51

335

74

98

6

710

29

539

52

324

75

88

7

692

30

531

53

313

76

78

8

680

31

523

54

302

77

68

9

670

32

51 5

55

202

78

58

10

661

33

507

56

282

79

49

11

653

34

499

57

272

80

41

12

646

35

490

58

262

81

34

13

640

36

481

50

252

82

28

14

634

37

472

60

242

S3

23

15

628

38

463

61

232

84

20

16

622

39

454

62

222

85

15

17

616

40

445

63

212

86

11

18

610

41

436

04

202

87

8

19

604

42

42/

65

192

88

5

20

598

43

417

66

1S2

89

3

21

592

44

407

G7

172

90

1

22

586

45

397

68

162

91

0

23

579

46

387

69

152

As there is allowed to be a till none be left, in order to form a greater disparity between births table particularly suited to this poand burials in the city of London, pulous city.

than in any other place. The following is Mr. Simpson' son selects 1280 persons, all born table on the bills of mortality, at in the same year, and records the London : number remaining alive each year,

Age. 0

Persons living.

Age.

Persons living.

Age. 48

Persons living.

Age

Persons living..

1280

24

434

220

72

59

1

8/0

25

426

49

212

73

54

2

700

26

418

50

204

74

49

3

635

27

410

51

196

75

45

4

600

28

402

52

188

76

41

5

580

29

394

53

180

77

38

6

564

30

385

54

172

78

35

7

551

31

376

55

165

79

32

8

541

32

367

56

158

80

29

9

532

33

358

57

151

81

26

10

524

34

349

58

144

82

23

11

517

35

340

59

13/

S3

20

12

510

36

331

60

130

84

17

13

504

37

322

61

123

S5

14

14

498

38

313

62

117

86

12

15

492

39

304

63

111

87

10

16

486

40

204

64

105

S3

8

17

480

41

284

65

99

89

6

13

4/4

42

274

66

93

90

5

19

463

43

264

67

87

91

4

20

462

44

255

68

81

92

3

21

455

45

246

69

75

93

2

22

448

46

237

70

69

94

1

23

441

47

228

71

64

95

0

But these tables, however perfect they may be in themselves, must be considered only as probable conjectures, founded on the usual period of human life, which is estimated as follows:

1. The probability that a person of a given age may live a certain number of years, is measured by the proportion which the number cf persons living at the proposed age bears to the difference between the said number, and that of persons existing at the given ages.

Thus, if it be required to know what chance a person 40 years of age may have to live seven years longer, the reader should refer to Dr. Halley's table, and from445, the number of persons living at 40 years of age, subtract the number of persons living at 47 years of age, and the remainder, being 68, will be the number of those who hi died during those seven years. The probability, that the person in ques-tion will live these seven years, is in the proportion of 377 to 68, or nearly as 51/2 to 1. By Mr. Simpson's table, the chance is somewhat less than that of 4 to 1.

If it be desirable to ascertain the year, which a person of a given age has an equal chance of attaining, the inquirer ought to find half the number of persons living at that given age, in the tables; and the year required will appear in the column of ages.

The premium of insurance upon lives may also, in some degree, be regulated by these tables, as follows :

The chance which a person of 25 years has to live another year, is, by Dr. Halt.ey's table, as 80 to 1 ; but the chance that a person of 50 years has to live a year longer, is only 30 to 1 ; and consequently the premium for insuring the former ought to be the premium for insuring the latter for one year, as 30 to 80, or as 3 to 8.

Life-annuities are commonly bought or sold at a certain number of years purchase. The value of an annuity of one pound for an age of 50 years at 3 per cent. interest, is about 12l. 10s. or twelve and a half years purchase,

Among those who have written on this subject, none is more deservedly celebrated than Dr. Price, the author of Observations on Reversionary Payments, Annuities, etc. published in 1771; and his curious remarks on this subject, inserted in the lxvth vol. of the Philos. Transactions, for 1775, p. 424, are well worthy of perusal and attention.

In our opinion, life annuities, when granted by individuals whose property is already involved, or who by such an expedient injure the just expectations of their relatives, ought not to be connived at in a well-regulated State.—Viewed in a commercial light, this species of gambling, in a certain degree resembles the furious rage for the hazard or pharo-table; to which all those adventurers and avaricious money - lenders generally resort, who are anxious to amass large sums of money, which, by moderate legal interest, could not be realized.