INTEREST. 
The infer cat for any greater number of dap 
than are contained in the table, is easily found 
by means of it ; thus, if it is required to find 
the interest of 100'. for 165 days, the interest for 
100 days by the table is 1,36986, and for 65 
days ,89011, which two sums added together, 
make 2,26027, or 21. 5s. 2 d. But, although it is 
most convenient in common practice to make 
use of tables for finding the interest for days, , 
the interest of any sum for any number of days 
may be correctly and expeditiously obtained 
without the use of any table, by the following 
rule : 
“ Multiply the given sum by the number of 
days, and divide by 7600.” 
Example 1. What is the interest of 3 561. for 
112 days ? 
356 multiplied by 112, and divided by 7300, 
gives 5,4619, or 51. 9s. 2±d. 
Example 2. What is the interest of 137/. 18 j. for 
97 days ? 
137,9 multiplied by 97, and divided by 7300, 
gives 1,8323, or 11. 16s. 7\d. 
The amount of a given sum in any time may 
be found by multiplying the Principal, Time, 
and Rate together ; and adding the product to 
the principal. 
Example 1. What sum will 37/. 10n amount to 
in 3 years and 146 days, at 4 per cent, per 
annum ? 
37,5 multiplied by 3,4, and the product mul- 
tiplied by ,04, gives 5,1 ; which added to 37,5, 
makes 42,6, or 42/. 12 s. 
Example 2. What sum will One Penny amount 
to m 1805 years, at 5 per cent, per annum? 
,004166 multiplied by 1806, and the product 
multiplied by ,05, gives ,37625, which, added 
to the principal, makes ,380-116, or 7s. 7 \d. 
This example sets the difference between sim- 
ple and compound interest in a most striking 
point of view ; it appears that one penny put 
out to interest at the birth of Christ, would (at 
5 per cent, simple interest) have amounted at 
the present time to 7s. 7\d., but at compound 
interest, it would have increased in the same 
period to a greater sum than would be con- 
tained in six hundred millions of globes, each 
equal to the earth in magnitude, and all solid 
goid. 
Interest, compound, is that which is reckoned 
on the principal and its interest put together, 
as the interest becomes due, so as to form a 
new capital from each period at which the in- 
terest is payable : it is sometimes called interest 
upon interest. It is not lawful to lend money 
at compound interest ; but in the granting or 
purchasing of annuities, leases, or reversions, it 
is usual to allow the purchaser compound in- 
terest for his money ; and the difference from 
simple interest is so great, in all cases in which 
the period of time is considerable, that almost all 
• computations relating to annual payments of 
money for a number of years, are made at com- 
pound interest, unless it is otherwise agreed. 
JLet r — the amount of 11. in one year, viz. 
principal and interest, 
n = the number of years, in which 
p — the principal, increases to 
a — the amount : 
then 1 * r ” r * r 2 the amount of 1/. in 2 years 
1 j r • r 2 \ r l the amount of 11. in 3 years 
1 | r [ " r 5 * r 4 the amount of 1/. in 4 years, 
& c.; 1 
therefore r", or r raised to the power whose 
exponent is the number of years, will be the 
amount of 1/. in those years ; and as 
11. ’ r‘ \ \ p \ a, the amount of a given princi- 
pui'iii the same. time. Thus, 
U Principal, Time, and Rate, are given, i( > Jind the 
Amount ? 
Theo. 1 . p X r — a. 
If Amount , Time, and Rate, are given, to fnd the 
Principal ? 
Theo. 2. 
If Principal, Amount, and Time, are given, to fnd 
the Rate? 
Theo. 3,- n 
/f- 
' P 
If Principal, Amount , and Rate, are given, to fnd 
the Time ? 
C — = r’ 1 , therefore — be- 
1 p p 
Theo. 4. < j n g d; v i<Ied by r till nothing 
I remains, the number of di- 
Lvisions will — n. 
But for greater convenience in practice, these 
theorems may be expressed in logarithms, as 
follows : ■ 
1. log. / -j- n X log. r — log. a. 
2. log. a — n X log. r — log /, 
log. a — log. / 
S. 
= log. 
log. a — log. / 
log- 
on these principles all tables of Compound 
Interest are formed, of which the following are 
the most useful. 
TABLE I. 
Shewing the Sum to which 1/. Principal will in- 
crease at 5 per Cent. Compound Interest, in 
any number of years not exceeding a hundred. 
In order to find what any sum will amount to 
dn a given number of years, it is only necessary 
to multiply the number in the Table opposite to 
29 
the term of years by the sum, and the product 
wil) he the answer. 
Example. To what sum will 50/. increase in 69 
years, at 5 per cent, compound interest ? 
The number in the table corresponding with 
69 years is 28.977548, which multiplied by 50, 
gives 1448.8774, or 14-18/. 17 j. 6d. 
The number of years in which a given surrL 
will increase 10 another given sum in conse- 
quence of being improved at interest, is found 
by dividing the latter sum by the former, and 
the sum in" the table which is nearest to the quo- 
tient will shew the term required. 
Example. In what time will 100/. increase to 
500/., it improved at 5 per cent. ? 
Divide 500 by 100, and the number in the 
table nearest to 5 the quotient, is 5.003188^ 
which shews that 33 years is the answer. 
TABLE II. 
Shewing the present Value of 1/. to be received 
at the end of any number of years, not ex- 
ceeding 100; discounting at 5 per Cent. Com- 
pound Interest. 
Yrs. 
Amount. 
Yrs. 
Amount. 
Yrs. 
Amount. 
1 
1.05 
35 
5.516015 
69 
28.977548 
O 
1.1025 
36. 
5.791816 
70 
30.426425 
3 
1.157625 
37 
6.081406 
71 
31.947746 
4 
1.215506 
38 
6.385477 
72 
33.545134 
5 
1.276281 
39 
6.704751 
73 
35.222390 
6 
1.340095 
40 
7.039988 
74 
36.983510 
7 
1.407100 
41 
7.391988 
75 
38.832685 
8 
1.477455 
42 
7.761587 
76 
■ 40.774320 
9 
1.551328 
43 
8.149666 
77 
42.813036 
10 
1.628894 
44 
8.557150 
78 
44.953688 
11 
1.710339 
45 
8.985007 
79 
47.201372 
12 
1.795856 
46 
9.434258 
80 
49.561441 
13 
1.885649 
47 
9.905971 
81 
52.039513 
14 
1.979931 
48 
10.401269 
82 
54.641488 
15 
2.078928 
49 
10.921333 
83 
57.373563 
16 
2.182874 
50 
11.467399 
84 
60.242241 
17 
2.292018 
51 
12.040769 
85 
63.254353 
18 
2.406619 
52 
12.642808 
86 
66.417071 
19 
2.526950 
53 
13.274948 
87 
69.737924 
20 
2.623297 
54 
13.938696 
88 
73.224820 
21 
2.785962 
55 
14.635630 
89 
. 76.886061 
22 
2.925260 
56 
15.367412 
90 
80.730365 
23 
3.071523 
57 
16.135783 
91 
84.766883 
24 
3.225099 
58 
16.942572 
92 
89.005227 
25 
3.386354 
59 
17.789700 
93 
93.455488 
26 
3.555672 
60 
18.679185 
94 
98.128263 
'27 
3.733456 
61 
19.613145 
95 
103.034676 
28 
3.920129 
62 
20.593802 
96 
108.186410 
29 
4.116135 
63 
21.623492 
97 
113.595730 
30 
4.321942 
64 
22.704667 
98 
119.275517 . 
31 
4.538039 
65 
23.839900 
99 
125.239293 
32 
4.764941 
66 
25.031895 
100 
131.501-257 
33 
5.003188 
67 
26.283490 
34 
5.253347 
68 
27.597664 
Yrs. 
Value. 
Yrs 
Value. 
Yrs. 
Value. 
1 
.952381 
pyj 
.181290 
69 
.034509 
2 
.907029 
36 
.172657 
70 
.032866 
3 
.863838 
37 
.164436 
71 
.031301 
4 
.822702 
38 
.156605 
72 
.029811 
5 
.783526 
39 
.149148 
73 
.028391 
6 
.746215 
40 
.142046 
74 
.027039 
7 
.710681 
41 
.135282 
7.5 
.025752. 
8 
.676839 
42 
.128840 
76 
.024525 
9 
.644609 
43 
.122704 
77 
.023357 
10 
.613913 
44 
.116861 
7S 
.022245* 
11 
.584679 
45 
.111297 
79 
.021186 
12 
.556837 
46 
.105997 
SO 
.020177 
13 
.530321 
47 
.100949 
81 
.019216 
14 
.505068 
48 
.096442 
82 
.018301 
15 
.481017 
49 
.091564 
83 
.017430 
16 
.458112 
50 
.087204 
84 
.016600' 
17 
.436297 
51 
.083051 
85 
.015809 
18 
.415521 
52 
.07909 6 
86 
.015056 
19 
.395734 
53 
.075330 
87 
.014339 
20 
.376889 
54 
.075743 
88 
.013657 
21 
.358942 
55 
.068326 
89 
.013006 
22 
.341850 
56 
.065073 
90 
.01 2387 
23 
.325571 
57 
.061974 
91 
.011797 
24 
.310068 
58 
.059023 
92 
.011235 
25 
.295303 
59 
.056212 
93 
.0/0700 
26 
.281241 
60 
.053536 
94 
.010191 
27 
.267848 
61 
.050986 
95 
.009705 
28 
.255094 
62 
.048558 
96 
.009243 
29 
.242946 
63 
.046246 
97 
.008803 
30 
.231377 
64 
.044044 
98 
.008384 
31 
.220359 
65 
.041946 
99 
.007985 
32 
.209866 
66 
.039949 
100 
.007604 
33 
.199873. 
67 
.038047 
34 
.190355 
68 
.036235 
In order to find the present worth of any sum 
which is to be received at the end of a certain 
number of years, multiply the number in the 
table opposite to the term of years, by the sum, 
and the product will be the answer. 
Example. What is the present value of 500/. to- 
be received at the expiration of 14 years ? 
The number in the table corresponding with. 
14 years, is .505068, which multiplied by 500, 
gives 252,534, or 252/. 10 j. 8 d. 
For the present value or amount of annual! 
pavments, as Annuities, Pensions, Leases, &c.. 
at Compound Interest, see Annuities. 
Interest, in law, is generally taken fora 
chattel real, or a lease for years, &c. but 
more for a future term. 
An estate in lands, &c. is better than a 
bare interest therein ; yet, according to the 
legal sense of the word, an interest extends to. 
