A- R I T H 
The Amount of 
il. in any number of Years. 
Yrs. 
3 
3§ 
4 
1 4i 
1 5 
6 
I 
I 0 O3OO 
1-0350 
I ”0400 
1 -0450 
I *0500 
1 -0600 
2 1 
1-0609 
I *07 I 2 
1 -0816 
I *0920 
1-1025 
1-1236 
3 
I "0927 
1-1087 
1-1249 
I “141 2 
1-1576 
I*I9I0 
4 
I "i 2 55 
1 ' 1 47 5 
1-1699 
1-1925 
*‘ 2 *55 
1-2625 
5 
i-i593 
1-1877 
1-2167 
1 -2462 
1*2763 
1 -3382 
6 
1-1941 
1-2293 
1-2653 
1-3023 
1*3401 
1-4185 
7 
1-2299 
1-2723 
1-3159 
1 -3609 
1-407* 
1 "5 0 36 
8 
1-2668 
1-3168 
i -3686 
I ‘4221 
1-4775 
1-5939 
9 
1-3048 
1-3629 
i-4 2 33 
1 -4861 
I-55I3 
1-6895 
10 
1*3439 
1-4106 
1-4802 
2-5530 
1 -6289 
1-7909 
11 
1 *3842 
1"4600 
1-5395 
1 -6229 
1-7103 
1-8983 
12 
1-4258 
1 ‘5 111 
1 -6010 
1-6959 
1’7959 
2*0122 
13 
1-4685 
1-564° 
1-6651 
1-7722 
1-8856 
2-1329 
-T4 
1-5126 
1-6187 
2*73*7 
1-8519 
i- 9799 
2*2609 
15 
i\ 55 8 ° 
1-6753 
1 -8009 
1-9353 
2-0789 
2*3966 
16 
1-6047 
1-7340 
1-8730 
2-0224 
2-1829 
2-5404 
17 
1-6528 
1-7947 
1-9479 
2-1134 
2°2920 
2-6928 
18 
1 -7024 
1-8575 
2-0258 
2-2085 
2-4066 
2-8543 
19 
1-7535 
1-9225 
2‘1068 
2-3079 
2-5270 
2-0256 
20 
1 -8061 
1-9898 
2-I91 I 
2-4117 
2-6533 
2 0 207I 
The life of this Table, which contains all the powers 
R™, to the 20th power, or the amounts of il. is chiefly to 
calculate the interefl, or the amount, of any principal fum, 
for any time, not more than twenty years. For example, 
required to find to how much 523I. will amount in fifteen 
years, at the rate of 5I. percent, per annum Compound 
Interefl. In the Table, on the line 15, and column 5 per 
cent, is the amount of il. viz. 2-0789, 
this multiplied by the principal - 523, 
gives the amount - - 1087-2647, or 
1087I. 5s. 3^d. and therefore the interefl is 564I. js. 3|d. 
See Algebra, vol. i. p.308 ; and Annuities, vol. i. 
P- 737 J and the article Interest. Alfo Smart’s Tables 
of Interefl, and the Philof. Tranf. vol.vi. p. 508. 
DISCOUNT. 
M E T 1 C. 
As the fum of the two produfts 412 : 400 :: 463I. 10s. 
: 450I. prefent worth. 
When goods are bought and fold, and difcount to be 
made for prefent payment at any rate per cent, without 
any regard to time, the interefl of the fum as calculated 
for one year, is the difcount. 
Ex. Bought goods to the value of 125L 14s. yd. dif¬ 
count at 5 per cent, what is the difcount and prefent worth > 
Fir ft 125I. 14s. 7d.X5~i°o=6l. 5s. 8£d. the difcount. 
And 125I. 14s. 7d.—61. 5s. 8^d.=1191. 8s. io£d. pre¬ 
fent money. 
EQUATION of PAYMENTS, 
A rule that teacheth, when feveral fums of money are 
due at different periods, to find the time when the whole 
may be paid at once without lofs to the debtor or creditor. 
Rule. Multiply every payment by the time it is to 
continue in the hands of the debtor, and divide the fum 
of the products by the fum of all the payments or whole 
debt; the quotient is the true equated time. 
Ex. A owes B 336I. whereof 150b is to be paid at two 
years end, 120I. at 3A years end, and 60I. at 44. years end ; 
at what time may the whole be paid together without pre¬ 
judice to either party ? 
f 2 X 150=3001 
Thus < 3^-x 120=420 5 the products. 
1.42 X 60—270J 
330)990(3 years from the beginning, or 
one year and a half from the time of the laft payment be¬ 
coming due; therefore three years is the true equated time. 
As may be thus proved : 
The amount of 150I. at 5 percent, for li") 
1. 
s. d. 
years, viz. tire interval between its becoming l 
due and the laft payment J 
168 
15 0 
The amount of 120I. for one year 
To which add the laft payment, on which 1 
2 26 
60 
0 0 
no intereft is due - - J 
0 0 
Amount of the feveral fucceffive payments 354 15 o 
The amount of the whole debt (300I.) for't 
year, viz. the interval between the equated l 354 15 o 
time and laft payment J 
This is an allowance made for the payment of any fum 
©f money before it becomes due, and is the difference of 
that fum due fome time hence, and its prefent worth. If 
the prefent worth be put out to intereft for the time, and 
at the rate for which the difcount is to be made, it would 
amount to the fum or debt then due. 
Rule. Multiply the time by the rate of intereft ; alfo 
multiply one year by 100 (taking the year in the fame de¬ 
nomination as the time propofed in the queftion), add the 
two produfts together, and by the Rule of Three fay, As 
the fum of the two products is to the former of the two 
products, fo is the fum to be difcounted to the difcount; 
which taken from the fum to be difcounted will leave its 
prefent worth. Or thus: As the fum of the two pro¬ 
ducts is to.the latter of the two produfts, fo is the fum to 
be difcounted to the prefent worth, in the fame denomina¬ 
tion as the fum to be difcounted. 
Ex. 1. What is the difcount and prefent worth of 1657I. 
10s. due fix years hence, at 5 per cent, per annum? 
Thus / 6x 5 — 30 fi rft product 
\1X100—100 fecond produCt 
Sum of the two produfts =130 
As 130: 
{ 
30 :: 
ioo :: 
1657I. ios. : 382I. 10s. difcount 
1657 10 : 1275 o prefent worth 
Proof 1657 10 
Ex. a. What is the prefent worth of 463I. 10s. for nine 
months, or three-qudrters of a year, at 4 per cent, per 
annum difcount ? 
Thus/ 3 * 4= 12 firft produft \ 
t4X 100=400 leoond product J 
412 
SINGLE FELLOWSHIP. 
Fellowfhip, Company, or Partner (hip, is a rule which 
determines how much gain or lofs is due to each partner 
concerned, by having the whole gain or lofs, and their 
particular (locks,given. Then, by the Rule of Three, As 
the whole (lock is to the whole gain or lofs, fo is eacli 
man’s particular (hare to his particular part of the gain 
or lofs. 
Ex. 1. Four perfons enter into partnerfhip, A puts in 
24I. B. 35I. C 40I. and D 37I. they gain 27I. 4s. what is. 
each man’s (hare ? 
Firft 24-1*35-440-1-37=1361. the whole (lock. 
And 27I. 4s. = 544s. the whole gain. Then 
1. s. 1. s. 
As 136-I. : 544s. :: 
Or as 1 : 4 :: 
Proof 
96 = 4 16 AV 
140 =7 o B’s 
160 = 8 o C’s 
148 = 7 8 P’s J 
27 4 whole gain. 
► gain. 
Having the whole flock, and gain or lofs, given, and 
each perfon’s gain or lofs, to find his flock. Say, as the 
whole gain or lofs is to the whole (lock, fois each perfon’s 
gain or lofs to his particular (lock. This is the mod in¬ 
fallible proof of the firft rule. 
Ex. 2. Four perfons traded a certain time with a joint 
flock of 136I. and gained 27I. 4s. of which A’s part was 
4I. 16s. B’S7l. C’s-81. and D’s 7I. 8s. what was each per-, 
Ton’s (lock ? 
As 544s. : 136I. :: 
Or 4 t 1 :: 
35 p," tftock. 
: 40 C’s j 
; 37 D’sJ 
Ex,. 
