INTEREST. 
.1 
If tiie principal, amount, and rate are 
given, to find the time ? 
f 2 = r n , therefore - being di- 
I P P 
Theo. 4. { vided by r till nothing re- 
| mains, the number of divi- 
k visions will be n. 
It seldom happens, however, that it is ne- 
cessary to work questions relative to com- 
pound interest by these rules, as very ex- 
tensive and accurate tables have been pub- 
lishes! by Mr. John Smart and others, which 
save much labour in such calculations, and 
are therefore generally resorted to in prac- 
tice. The principles on which such tables 
are formed will appear from what has been 
already said : thus, tiie numbers in a table 
shewing the amount of 1 l. in any given 
number of years, are inerely the powers of 
11. increased by its interest for a year ; that 
is, r, r 2 , r s , r 4 , &c. and the numbers con- 
tained in a table of the present values of 11. 
to be received at the end of a given number 
of years, are 11. discounted for those years, 
or 11. divided by the powers of r, that is, 
1111 
r 21 ,7s) ~4> & C - 
Tables of this kind being usually con- 
fined to six or eight places of decimals, ne- 
cessarily give the amount beyond the first 
three or four years somewhat less than the 
true amount, but the difference is so small 
as to be of no importance in the purposes 
to which they are usually applied. 
TABLE I. 
Shewing the Sum to which 11. Principal will increase at 5 per Cent Compound Inte- 
rest, in any Number of Years not exceeding a Hundred. 
Years. 
Amount. 
Years. 
Amouut. 
Years. 
Amount, 
Years. 
Amount. 
i 
1.05 
26 
3.555672 
51 
12.040769 
76 
40.774320 
2 
1.1025 
27 
3.733456 
52 
12.642808 
77 
42.813036 
1457625 
28 
3.920129 
53 
13.274948 
78 
44.953688 
4 
1.215506 
29 
4.116135 
54 
13.938696 
79 
47.201372 
5 . 
1,276281 
30 
4.321942 
55 
14.635630 
80 
49.561441 
6 
1.340095 
31 
4.538039 
56 
15.367412 
81 
52.039513 
7 
1.407100 
32 
4.764941 
57 
16.135783 
82 
54.641488 
8 
1.477455 
33 
5.003183 
58 
16.942572 
83 
57.373563 
9 
1.551328 
34 
5.253347 
59 
17.789700 
84 
60.242241 
10 
1.628894 
35 
5.516015 
60 
18.679185 
85 
63.254353 
11 
1.710339 
36 
5.791816 
61 
19.613145 
86 
66.417071 
12- 
1.795856 
37 
6.081406 
62 
20.593802 
87 
69.737924 
13 
1.885649 
38 
6.38547 7 
63 
21.623492 
88 
73.224820 
14 
1.979931 
39 
6.704751 
64 
22.704667 
89 
76.886061 
15 
2.078928 
40 
7.039988 
65 
23.839900 
90 
80.730365 
16 
2.182874 
41 
7.391988 
66 
25.031895 
91 
84.766883 
17 
2.292018 
42 
7.761587 
67 
26.283490 
92 
89.005227 
18 
2.406619 
43 
8.149666 
68 
27.597664 
93 
93.455488 
19 
2.526950 
44 
8.557150 
69 
28.977548 
94 
98.128263 
20 
2.653297 
45 
8.985007 
70 
30.426425 
95 
103.034676 
21 
2.785962 
46 
9.434258 
71 
31.94774 6 
96 
108.186410 
22 
2.925260 
47 
9.905971 
72 
33.545134 
97 
113.595730 
23 
3.071523 
48 
10.401269 
73 
35.222390 
98 
119.275517 
24 
3.225099 
49 
10.921333 
74 
36.983510 
99 
125.239293 
25 
3.386354 
50 
11.467399 
75 
38.832685 
100 
131.501257 
Ex. 1. What sum will 500 1. increase to in 
21 years, if improved at .5 per cent, com- 
pound interest ? 
500 X 2.785962 = 139 Si. 19s. 7\d. 
Ex. 2. What sum, if improved at 5 per 
cent, compound interest will accumulate to 
a million in 50 years ? 
100 °y )0 - =872031. 14s. 8d. 
11.467399 
The increase of an annuity, ifforbornefor 
a given time, may be found by this table 
in the same manner as the amount of a 
given sum, for as each payment of the an- 
nuity will become due at an equal distance 
from thq time in which it would have been 
due, the amount of the first payment must 
give that of each of the succeeding ones. 
Ex. 3. A person being entitled to an an- 
