ANN 
TABLE II. 
The prefent Value of an Annuity of il. 
at 3 per 
oi P er 
4 Per 
4 k per 
5 Per 
6 per 
“ 
cent. 
cent 
c-nt. 
cent. 
cent. 
cen*. 
1 
0-97087 
0-96613 
0-96154 
0-95694 
0-95238 
0-94340 
2 
1-91347 
t -89969 
r886io 
1-87267 
1-85941 
1-83339 
3 
2-82861 
2-80164 
2-77509 
2-74896 
2-72325 
2-6730. 
4 
3-71710 
3-57308 
3-62990 
3-58753 
374595 
3-4651.- 
5 
4-57971 
4 ’ 5 1 5°5 
4-45182 
4-38998 
4-32948 
4-21236 
6 
5-41719 
5-32855 
5-24214 
5-15787 
5-07569 
4-91732 
7 
5-23028 
6-11454 
6-00205 
5-89270 
5-78637 
5-5823;-, 
8 
7-01965 
6-87396 
&73274 
6-59589 
6-46321 
6-20979 
9 
7-78611 
7-60769 
7-43533 
7-20879 
7-10782 
6-80109 
IO 
8-5302° 
8"31 56 1 
8-11090 
7-91272 
772173 
7-36009 
77 
q-25202 
9-00155 
8-76048 
8-52892 
8-30541 
7-8808' 
12 
9-95400 
9-66333 
9 - 3 B 507 
9-11858 
8-86325 
8-38384 
■ 3 
10-63496 
10-30274 
9-98565 
9-58285 
9*39357 
8-85268 
if 
i 1-29607 
10-92052 
10-50312 
10-22283 
9-89864 
9-29498 
IS 
n -93794 
11-51741 
11-11839 
1073955 
10-37966 
9-71225 
iii 
12-56110 
12-09412 
11 -65230 
11-23402 
io- 83777 ji°- I0 59 o 
17 
13•16612 
12-65132 
12-16567 
11-70719 
11-27407110-47726 
18 
' 3-75351 
13-18968 
12-65930 
12-15999 
11-68959 10-82760 
19 
14-32380 
1370984 
13 ->3394 
12-59329 
12-08532! 11-15812 
20 
14 - 3774 :' 
1 (.-21240 
i 3 ‘S 9033 
13-00794 
12-46221 
I ! -46992 
21 
15.41502 
14-69797 
14-02916 
13-40472 
12-82115 
1 I -76408 
22 
I 5 ' 9369 2 
15-16712 
14-45112 
1378442 
13-16300 12-04159 
z 3 
16-44361 
15-62041 
14-85684 
I 4-14777 
I 3-48357 
12-30338 
z 4 
16 ' 9355 -i 
16-05837 
15-13696 
14-49548 
13-79864 
12-55036 
25 
I 7 ' 4 I 3 1 S 
16-48151 
13-62208 
14-82821 
iro 9394 
1278336 
26 
1707634 
16-89035 
15-98277 
15-14661 
14-37519 
13-00317 
18-32703 
17-28536 
16-32959 
1 5 ’ 45 130 
I 4 ' 6 43°3 
13-21053 
28 
1876411 
17-66702 
16-66306 
1474287 
14-89813 
13-40616 
29 
19-18845 
18-03577 
16-98371 
16-02189 
15-14107 
13-59072 
3 ° 
19-00044 
18-39205 
17-29203 
16-28889 
I 5-37245 
I376483 
U 
20-00043 
18-73625 
17-58849 
16-5443 
15-59281 
13-9290, 
20-38877 
[9.06887 
17-87355 
1678889 
15-80268 
14-0840.1 
33 
20-76579 
19-39021 
18-14765 
17-02286 
16-00255 
14-23023 
34 
21-13184 
19-70068 
18-41120 
17-24676 
16-19290 
14-36814 
33 
21-48722 
20-0006 
18-66461 
17-46101 
16-37419 
14-49825 
3 : 
21-83225 
2 O- 2 Q 04 Q 
18-90828 
17-06604 
16-54685 
14-62099 
37 
22- 1672-; 
20-5-053 
19-14258 
17-86224 
16-71129 
14-73678 
3 B 
22-49240 
20-84:09 
19-36786 
18-04999 
16-86789 
14-84602 
3 - 
22-8o822 
21*102^0 
19-58448 
18-2296:; 
17-01704 
14 - 9+907 
4 o 
23 I 1477 
21 ■ 355 0 7 
1979277 
18-4015? 
17- 1 5909 
15-04630 
41 
23-41240 
21 -59910 
19-99305 
18-56611 
17-29437 
15-13802 
4 2 
23 ' 70 I 3 (l 
2I-8348.- 
20-1856; 
1872355 
17-42321 
I 5-22454 
43 
’.3-98190 
22-06269 
’0-37079 
18-87421 
I 7 - 5459 I 
15-30617 
44 
24-25427 
22-28270 
20 54884 
19-01838 
17-66277 
15-38318 
45 
22-49545 
20-72004 
19-15635 
17 77407 
15-45583 
47 
24-77545 
22-70092 
20-88465 
19-28837 
17-88007 
15-52437 
47 
2 5 - 0247 I 
22-89944 
21 -04294 
19-41471 
17-98102 
15-5890 
4 ' 
A 5'2667 S 
23-09124 
21-19513 
19-53561 
18-07716 
! 5-6500; 
49 
25-50166 
23-27656 
21-34147 
19-65130 
18-16872 
■■ 5-707 5 ' 
5 c 
2 f 7 Z 976 
2 C 455 62 
21-48218 
19-76201 
18-25593 
15 76186 
5 * 
25-95123 
23-62862 
21-6174^ 
19-86:95 
18-33898 
I 5 - 8 I 308 
52 
26-I0624 
2379576 
21-74758 
19-9693. 
18-41807 
15 - 85 I 39 
53 U&- 3749 ? 
z 3 - 9572 f 
21-87267 
20-06635 
18-49340 
15-9067 
54 
|z 6-57766 
24-11330 
21-99296 
20-15918 
'8-505:5 
15-94998 
The Use of Table I. 
To find, the Amount of an Annuity forlorn any number of 
Years. Take out the amount from the firit table, for the 
propofed years and rate of intereft; then multiply it by 
the annuity in queftion ; and the produCt will be its amount 
for the fame number of years, and the rate of intereft. 
And the converfe to find the rate or time. 
Exam. i. To find how much an annuity of 50I. will 
amount to in 20 years at 3^ per cent, compound intereft. 
On the line of 20 years, and in the column of 3A percent, 
hands 28-27.968, which is the amount of an annuity of il. 
ANN 739 
for the 20 years; and therefore 28-27968, multiplied by 
50, gives 1413.984I. or 1413I. 19s. 8d. for the anfwer. 
Exam. 2. In what time will an annuity of 20I. amount 
to ioool. at 4 per cent, compound intereft? Here the 
amount of ioool. divided by 20I. the annuity, gives 50, 
the amount of il. annuity for the fame time and rate. 
Then, the neareft tabular number in the column of 4 per 
cent. 1549-96758, which, handing on the line of 28, (hews 
that 28 years is the anfwer. 
Exam. 3. If it be required to find at what rate of in¬ 
tereft an annuity of 20I. will amount to ioool. forborn for 
28 years. Here 1000 divided by 20 gives 50 as before; 
then looking along the line of 2S years, for the neareft to 
this number 50, I find 49’96758 in the column of 4 per 
cent, which is therefore the rate of intereft required. 
The Use of Table II. 
Exam. i. To find the prefent value of an annuity of 
50I. which is to continue 20 years, at 3 a per cent. By the 
table, the prefent value of il. for the fame rate and time, 
is 14-21240; therefore 14-2124X S°—l io - 62l. or 710I. 
12s. 4d. is the prefent value fought. 
Exam. %. To find the prefent value of an annuity of 20I. 
to commence 10 years hence, and then to continue for 40 
years, or to terminate 50 years hence, at 4 per cent, in¬ 
tereft. In Inch cafes as this, it is plain we have to find the 
difference between the prefent values of two equal annui¬ 
ties for the two given times ; which therefore will be ef¬ 
fected by fubt ratting the tabular value of the one term 
from that of the other, and multiplying by the annuity. 
Thus, 
Tabular value for 50 years 21’48218 
Tabular value for 10 years 8-11090 
The difference 13 37128 
Multiply by 20 
Gives 267-4256, or 267I. 8s. 6cl, 
[the anfwer. 
The foregoing obfervations, rules, and tables, contain 
all that is important in the doctrine of annuities certain. 
And, for farther information, reference may be had to 
arithmetical writings, particularly Malcolm's Arithmetic, 
page 595; Simpfon’s Algebra, fett. 16 ; Dodfbn’s Mathe¬ 
matical Repofitory,. page 298, &c. Jones’s Synopfis, ch, 
104 Philof. Traf. vol. lxvi. page 109. 
For what relates to the doctrine of annuities on lives, fee 
Assurance, Complement, Expectation, Life An¬ 
nuities, See. 
To ANNU'L, v. a. [from vullus, Lat.] To make void; 
to nullify; to abrogate; to aboljlh.—That which gives 
force to the law, is the authority that enacts it ; and who¬ 
ever deftroys this authority, does, in effect, annul the law. 
Rogers. To reduce to nothing ; to obliterate; 
Light, the pure work of God, to me’s extinCt,- 
And all her various objeCts of delight 
Annulled, which might in part my grief have eas’d. Milton. 
AN'NULAR, adj. [annulus, Lat.] Something in the 
form of, or refembling, a ring. It is alto a peculiar de¬ 
nomination of the fourth finger, commonly called the 
ring-finger. 
AN'JN’ULARY, adj. [annulus, Lat.] In the furm of 
rings. — Becaufe continual refpiration is neceffary, the 
wind-pipe is made with annulary cartilages, that the fides 
of it may not Hag and fall together. Ray. 
AN'NULET,yi [annulus, Lat.] a littl'e ring.—In he¬ 
raldry, a difference or mark of diftinttion, which the fifth 
brother of any family ought to bear in his coat of arms. 
Annulets are alfo a part of the coat-armour of feveral fami¬ 
lies ; they were anciently reputed a mark of nobility and 
jurifdittion, it being thecuftom of prelates to receive their 
inveftiture per baculum & annulum. —In architecture, the 
fmall fquare members in the Doric capital, under the 
quarter round, are called annulets. Annulet is alfo ttfed for 
a narrow 
