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vided by that power of the ratio denoted by the time, minus unity will give the annuity.

Or, Divide the continual product of the present worth, that power of the ratio denoted by the time of continuance, that power of it denoted by the time of reverfion, and the ratio minus 1, by that power oi the ratio denoted by the time of continuance minus 1, and the quotient will be the annuity.

EXAMPLES.

1. What annuity, to be entered upon 2 years hence, and then to continue 4 years, may be purchased for £185,035876 at 61. per cent. ?

Method 1.-185,036×1,1236 =207,906

Then 207,906X1,33822-207,906X1,26247

1,26247-1

60 (Ans.

Or, by Table IV. Divide the present worth of the reverfion by the difference between the present worth of 11. for the time both in being and reverfion, and the time in being, and the quotient will be the annuity.

Meth 2. 185,036Χ1,26247Χ1,1236×1,06-1

1,26247-1

= 60.

2. The present worth of a leafe of a house is 4311. 15s. 7d. 2.78 9qrs. taken in seversion for 20 years, but not to commence until the end of 8 years, allowing 61. per cent. to the purchaser; What is the yearly rent ? Ans. £60.

TABLE

TABLE FIRST.

Shewing the amount of Il. from 1 year to forty years.

ys 5 per cent. 6 per cent. ys 5 per cent. 16 per cent 1/1,0500000 1,0600000 21 2,7859625 3,3995636 21,1025000 1,1236000 22 2,9252607 3,6035374 31,1576250 1,1910160 23 3,0715237 3,8197496 41,21550621,2624769 243,2250999 4,0489346 51,27628151,3382256253,3863549 4.2918707 61,34009561,4185191 263,5556716 4,7493829 71,40710041,503630227.3,7334563 4,8223459 81,47745541,5938480 28 3,9201291 5,1116867 91,5513282 1,6894789294,1161356 5,4183879 101,62889461,7908476 304,3219423 5,7434912 11 1,71032931,8982985 314,5380394 6,0881007 121,79585632,0121964 32 4,7649414 6,4533867 1,88564912,1329282 335,0031885

13

6,8405899

14 1,97993162,2609039 345,2533479 7,2510253 152,07892812,3965581 355,5160152 7,6860868 162,18287452,5472719 36 5,7918101 8,147252 172,29201832,6927727 376,0814069 8,6860871 182,40661922,8543391386,3854772 9,1542523 192,52695023,0255995396,7047511 9,7035074 202,6532977 3,2071355 407,0399887 10,2857178

TABLE

TABLE SECOND.

Sherwing the present Value of 11. due at the end of any num. ber of Years, from 1 to 40.

years 15pr.cent Oprocent. years. 5pr.cent. 16pr cent

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TABLE THIRD.

Shewing the amount of Il. annuity for any number of years, from 1 to 40.

ys. 5 per cent. 6 per cent. ys. 5 per cent. 16 per cent.

[blocks in formation]

2 2,05

1, 2,06

21 35,719252 39,992725

22 38,505214 43,392289 3 3,1525 3,1836 23 41,430475 46,995826 4,310125 4,374616 24 44,501999 50,815576 55,525631 5,637093 25 47,727009 54,86451 66,801913, 6,975318 26 51,1345459,156381

8,142008 8,393387 27 54,669126 63,705763 89,549109 9,897467/28 58,402583 68,528109 1,026564 11,491315/29 62,322712 73.639796 10 12,577892 13,180794 30 66,438847 79,058.83 1114,206787 14,971642 3170,76079 84,80.674 1215,917126 16,86994 32 75,298829 90,889775 117,71298318,882132 33 80,063771 97.343161 419,59863221,015064 34 85,06695904,183751 1521,57856323,275908 35 90,320307 111.434-76

25,84036628,212879 37 101,628139 127,268114

1623,657492 25,672527 36 95836323119,120863

1828,13238530,905652 38 107,709546 135,904201

1930,52900433,759991 39 114,095025145,058453

2033,06595436,78559 140 120,799774154,761961

TABLE

TABLE FOURTH.

Shewing the present worth of 11. annuity, for any number of years from 1 to 40.

ys. 5 per cent. 6 per cent. || ys. 15 per cent. 6 per cent.

1

2

0,95238 0,94339 21
1,85 4 1,83339 22

12,82115 11,76407 12,04158

13,163

3 2,72325 2,67301 23 13,48807 12,30338

24 13,79864 12,55035 14,09394 12,78335

43-54595 3:4651
5 4.3948 4.21236 25

65.07569 4,91732 26 14-37518 13,00316

75,78637 5.58238 27

8

14.64303 13,21053

6,4632 6,20979 28 | 14,898-3 13,40616

97,10782 6,80169 29

7,72173 7,36008 30

10

11 8,30641 7,88687 31

15,14107 13,59072 15.37245 13,76483 15,5928 13,92908

12

8,86325 8,38384 32 13 9,39357 8,85268 33

15,80268 14,08398

149,89864 9,29498 34

16,00255 14,22917 16,1929 14,36613

15 10,37966 9,71225 35

16,37419 14,49533

[blocks in formation]
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