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1067,50 amount.
200,00 first payment deducted.

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867,50 balance due, Feb. 19, 1798
70,845 interest to June 29, 1799-16 months

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938,345 amount. ,500,000 second payment deducted.

458,345 balance due, June 29, 1799.
26,30 Interest for one year.

464,645 amount for one year.
269,750 amount of third payment for 7 months.
194,895 balance due June 29, 1800. mo. da.

5,687 Interest to December 24, 1800. 5 25

200,579 balance due on the Note, Dec. 24, 1800.

. : RULE II. Established by the Courts of Law in Massachusetts you

computing interest on notes, &c. Or which partial par ments have been endorsed.

« Compute the interest on the principal sum, from the time when the interest commenced to the first time when a payment was made, which exceeds either alone or in conjunction with the preceding payment (if any) the in: terest at that time due: add that interest to the princi. pal, and from the sum subtract the payment made at that time, together with the preceding payment (if any) and the remainder forms a new, principal; on which compute and subtract the payments as upon the first principal, and proceed in this manner to the time of final settle

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•260,00 third payment with its interest from the time 9,75 was paid, up to the end of the year, orefrog,

- Nov. 14, 1799 to June 29, 1800, which is 73 869,75 amount

$200

Let the foregoing example be solved hy this Rule. A note for 1000 dols. dated Jan. 4, 1797, at 6 per cent

1st payment February 19, 1798. 2d payment June 29, 1799.

500 Sd payinent November 14, 1799.

260 How much remains due on said note the 24th of De. cember, 1800 ?

$ cts. Principal, January 4, 1797,

1000,00 Interest to Feb. 19, 1798, (13) mo.) 67,50

Amount, 1067,50 Paid February 19, 1798,

200,00 Remainder for a new principal,

867,50 Interest to June 29, 1799, (164 mo.) 70,84

Amount, 938,34 Paid June 29, 1799,

500,00 Remains for a new principal,

438,34 Interest to November 14, 1799, (4) mo.) 9,86

Amount, 448,20 November 14, 1799, paid i

260,00

Remains a new principal,
Interest to December 24, 1800, (134 mo.)
Balance due on said note, Dec. 24, 1800,

Scts.
The balance by Rule I. 200,579

By Rule II. 200,990

188,20

12,70 200,90

Difference, 0,411 Another Example in Rule II. A bond or note, dated February 1, 1800, was given for 500 dollars, interest at 6 per cent. and there were pay. ments endorsed upon it as follows, viz.

Scts. 1st payment May 1, 1800,

40,00 2d payment November 14, 1800

3d payment April 1, 1801.

· 12,00 4th payment May 1, 1801.

30,00 · How much remains due on said note the 16th of Septe tember, 1801 :

$ cts. Principal dated February 1, 1800,

500,00 Interest to May 1, 1800, (3 mo.)

7,50

. Amount, 507,50 Paid May 1, 1900, a sum exceeding the interest, 40,00 New principal, May 1, 1800,

467,50 Interest to May 1, 1801, (1 year.) . 28,05

Amount, 495,56 Paid Nov. 4, 1800, a sum less than the interest then due,

8,00 Paid April 1, 1801, do do. 12,00 Paid May 1, 1801, a sum greater, 30,00

50,00 New principal May 1, 1801,

445,55 Interest to Sept. 16, 1801, (41 mo.) 10,02 Balance due on the note, Sept. 16, 1801, $455,57

The payments being applied according to this Rule, keep down the interest, and no part of the interest ever forms a part of the principal carrying interest.

COMPOUND INTEREST BY DECIMALS.

RULE. MULTIPLY the given principal continually by the amount of one pound, or one dollar, for one year, at the rate per cent. given, until the number of multiplications are equal to the given number of years, and the product will be the amount required.

Or, In Table I. Appendix, find the amount of one dola lar, or one pound, for the given number of years, which multiply by the given principal, and it will going this amount as before.

EXAMPLES. 1. What will 4001. amount to in 4 years, at 6 per cent. per annum, compound interest ?

400 x 1,66x1,06 1,06x1,06=4504,99+ or
~ :." (6504 10s. 9d. 2,75grs. t Ans.

The same by Table I.
Tabular ainount of £1=1,26247
Multiply by the principal 400

Whole amount=4504,98800 l Required the amount of 425 dols. 75 cts. for 3 years, at 6 per cent, compound interest. Ans. $307,7 jcts. +

S. What is the compound interest of 355 dols. for 14 years, at 5 per cent. ? By Table I. Ans. 8543,86cts. +

4. What will 50 dollars amount to in 20 years, at 6 per cent, coinpound interest ? Ans. $160 35cts. 6fm.

INVOLUTION. Is the multiplying any number with itself, and that product by the former multiplier; and so on; and the several products which arise are called powers.

The number denoting the height of the power, is called tho index, or exponent of that power.

EXAMPLES
What is the 5th power of 8.

8 the root or 1st power.

64 = ld power, or square.

3d power, or crime

4th power, or biquadrate.

What is the square of 17,1 ?

Àns. 292,41 What is the square of ,085 ?

Ans. ,007225 What is the cube of 25,4 ?

Anš. 16387,064 What is the biquadrate of 12? Ans. 20736 What is the square of 777

Ans. 52

EVOLUTION, OR EXTRACTION OF ROOTS.

W HEN the root of any power is required; the busi.. ness of finding it is called the Extraction of the Root.

The root is that number, which by a continual multiplication into itself, produces the given power.

Although there is no number but what will produce a perfect power by involution, yet there are many numbers of which precise roots can never be determined. But, by the help of decimals, we can approximate towards the rout to any assigned degree of exactness.

The roots which approxiinate, are called surd roots, and those which are perfectly accurate are called rational roots.

A Table of the Squares and Cubes of the nine digits. Roots. T112 | 3 | 4 | 5 | 617 18 19 Squares. T1|4| 9 | 16 | 25 | 36 | 49 | 64 T 81 Cubes. 118 | 27 | 64 | 125 | 216 343 5127291

EXTRACTION OF THE SQUARE ROOT. Any nuinber multiplied into itself produces a square.

To extract the square root, is only to find a number, which being multiplied into itself, sliäll produce the given number.

RULE. 1. Distinguish the given number into periods of two figures each, by putting a point over the place of units, anuther over the place of hundre.'s, and so on; and it there arc decimals, point them in the same manner, Irown units lurvards the right handl; which points show Uic number of figures the rout will consist of.

2. Find the greatest square number in tlie first, or left

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