ANNUITIES. 
a similar nature, for different rates of in- 
terest which are given in most books on 
compound interest, save much time and 
labour in common practice, and are there- 
fore in general use. 
TABLE I. 
Shewing the amount of an annuity of 1 1. 
in any number of years not exceeding 
100, at 5 per cent, per annum compound 
interest. 
Yrs. 
Amo. 
Yrs. 
Amount. 
Yrs. 
Amount. 
1 
1,0000 
35 
90,3203 
69 
559,5510 
2 
2,0500 
36 
95,8363 
70 
588,5285 
3 
3,1525 
37 
101,6281 
71 
618,9549 
4 
4,3101 
38 
107,7095 
72 
650,9027 
5 
5,525(5 
39 
114,0950 
73 
684,4478 
6 
6,8019 
40 
1(20,7998 
74 
719,6702 
7 
8,1420 
41 
127,8393 
75 
756,6537 
8 
9,5491 
42 
135,2317 
76 
795,4864 
9 
11,0266 
43 
142,9933 
77 
836,2607 
10 
12,5779 
44 
151,1430 
78 
879,0738 
11 
14,2068 
45 
159,7002 
79 
924,0274 
12 
15,9171 
46 
168,6852 
80 
971,2288 
13 
17,7130 
47 
178,1194 
81 
1020,7903 
14 
19,5986 
48 
188,0254 
82 
1072,8298 
15 
21,5786 
49 
198,4267 
83 
1127,4713 
16 
23,6575 
50 
209,3480 
84 
1184,8448 
17 
25,8404 
51 
220,8154 
85 
1245,0871 
18 
28,1328 
52 
232,8562 
86 
1308,3414 
19 
30,5390 
53 
245,4990 
87 
1374,7585 
20 
33,0659 
54 
258,7739 
88 
1444,4964 
21 
35,7192 
55 
272,7126 
89 
1517,7212 
22 
38,5052 
56 
287,3482 
90 
1594,6073 
23 
41,4305 
57 
302,7157 
91 
1675,3377 
24 
44,5020 
58 
318,8514 
92 
1760,1045 
25 
47.7271 
59 
335,7940 
93 
1849,1098 
26 
51,1135 
60 
353,5837 
94 
194 2,5653 
27 
54,6691 
61 
372,26-29 
95 
2040,6935 
28 
58,4026 
62 
391,8760 
96 
2143,7282 
29 
62,3227 
63 
412,4698 
97 
2251,9146 
30 
66,4388 
64 
434,0933 
98 
2365,5103 
31 
70,7608 
65 
456,7980 
99 
2484,7859 
32 
75,2988 
66 
480,6379 
100 
2610,0252 
33 
80,0638 
67 
505,6698 
34 
85,0670 
68 
5o1,9di)i) 
Example 1. — To what sum will an an- 
nuity of 1051. amount in 19 years, at 5 per 
cent, compound interest? 
The number in the table opposite to 19 
years is 30,5390, which multiplied by 105 
gives the answer 32061. lls. lOd. 
Example 2. — In what time will an an- 
nuity of 251. amount to 35 751. at 5 per cent, 
compound interest? 
Divide 35751. by 251. the quotient is 143 ; 
the number nearest to this in the table is 
142,9933, and the number of years corres- 
ponding, or 43 years, is the answer. 
The present worth of an annuity, or the 
sum to be given in one present payment as 
an equivalent for an annuity for any given 
number of years, is found on similar prin- 
ciples ; for as 11. is the present value of r n 
(its amount in n years, and as the pre- 
sent value of any other amount, and conse- 
quently 
°f —y ~ — 1 must bear the same propor- 
tion to that amount, we have 
u 
Example. — W hat, is the present value of 
50 1. per annum for 6 years, at 5 per cent, 
compound interest? 
50 — 
50 
S ' < 
— 2531. 15s. 8(1. 
But such questions are much more readily 
answered by the following table. 
TABLE II. 
Shewing the present value of an annuity of 
1 1. for any number of years not exceeding 
100, at 5 per cent, per annum compound 
interest. 
Y. 
Value. 
Y. 
Value. 
Y. 
Value. 
1 
,952381 
35 
16,374194 
69 
19,309810 
2 
1,859410 
36 
16,546852 
70 
1 9,342677 
3 
2,723248 
37 
16,711287 
71 
19,373978 
4 
3,545950 
38 
16,867893 
72 
19,403788 
5 
4,329477 
39 
17,017041 
73 
19,432179 
6 
5,075692 
40 
17,159086 
74 
19,459218 
7 
5,786373 
41 
17,294368 
75 
19,484970 
8 
6,463213 
42 
17,423208 
76 
19,5094 95 
9 
7,107822 
43 
17,545912 
77 
19,532853 
10 
7,721735 
44 
17,662773 
78 
19,555098 
11 
8,306414 
45 
17,774070 
79 
19,576284 
12 
8,863252 
46 
17,880066 
80 
19,596460 
13 
9,393573 
47 
17,981016 
81 
19,615677 
14 
9,898641 
48 
18,077158 
82 
19,633078 
15 
10,379658 
49 
18,168722 
83 
19,651407 
16 
10,837770 
50 
18,255925 
84 
19,668007 
17 
11,274066 
51 
18,338977 
85 
19,683816 
18 
11,689587 
52 
18,418073 
86 
19,698873 
19 
12,085321 
53 
18,493403 
87 
19,713312 
20 
12,462210 
54 
18,565146 
83 
19,726869 
21 
12,821153 
55 
18,6334 72 
89 
19,739875 
22 
1 3, 163003 
56 
18,698545 
90 
19,752262 
23 
13,488574 
57 
18,760519 
91 
19,764059 
24 
13,798642 
58 
18,819542 
92 
19,775294 
25 
14,093945 
59 
18,875754 
93 
19,785994 
26 
14,375135 
60 
18,929290 
94 
19,796185 
27 
l4 7 643034 
61 
18,980276 
95 
19,805891 
28 
14,898127 
62 
19,028834 
96 
19,815134 
29 
15,141074 
63 
19,075080 
97 
19,823937 
30 
15,372451 
64 
19,119124 
98 
19,832321 
31 
15,592810 
65 
19,161070 
99 
19,840306 
32 
15,802677 
66 
19,201019 
100 
19,847910 
33 
16,002549 
67 
19,239066 
34 
16,192904 
68 
19,275301 
