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1067,50 amount.

[Brought up. 200,00 first payment deducted...

100
867,50 balance due, Feb. 19, 1798.
70,845 interest to June 29, 1799=164 months. '

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438,345 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 for

computing interest on notes, &'c. on which partial pay-
ments have been endorsed.'

6 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 interest at that time due: add that interest to the principal, and from the sum şubtract 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 settleinent."

S-cts. *260,00 third payment with its interest from the time it

9,75 was paid, up to the end of the year, or from

. Nov. 14, 1799 to June 29, 1800, which is 74 269,75 amount.

[months.

VIES

Let the foregoing example be solved by this Rule. À note for 1000 dols. dated Jan, 4, 1797, at 6 per cent. 1st payment February 19, 1798.

8200 2d payment June 29, 1799.

500 3d payment November 14, 1799.

260 How much remains due on said note the 24th of December, 1800 ?

8 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

i Amount, 938,54 Paid June 29, 1799,

500,00

Remains for a new principal,
Interest to November 14, 1799, (41 mo.)

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

260,00 Remains a new principal,

188,20 Interest to December 24, 1800, (13} mo.) 12,70 Balance due on said note, Dec. 24, 1800, 200,90

1 Scts. The balance by Rule I. 300,579

By Rule II. 200,990

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 paynents endorsed upon it as follows, viz. $ cts. (1st payment May 1, 1800,

40,00 2d payment November 14, 1800,

8,00

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$d payinent April 1, 1801.

12,00 4th payment May 1, 1801.

$0,00 How much remains due on said note the 16th of September, 1801 ?

$ cts. Principal dated February 1, 1800,

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

7,50

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

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

28,05
. .. Amount, 495,55
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, 6455,57

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

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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 dollar, or one pound, for the given number of years, which multiply by the given principal, and it will give the amount as before.

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

400X1,06X1,06x1,06X1,06=5504,99+ or

[£504 19s. 9d. 2,75yrs. + Ans.
The same by Table 1.
Tabular amount of £1=1,26247
Multiply by the principal 400

Whole amount=£504,98800
* %. Required the amount of 425 dols. 75 cts. for 3 years,
at 6 per cent. compound interest. Ans. $507,7 jcts. +

3. What is the compound interest of 555 dols. for 14
years, at 5 per cent. ? By Table I. Ans. $543,86cts. +

4. What will 50 dollars amount to in 20 years, at 6 per cent, compound interest ? Ans. $160 35cts. 65m.

INVOLUTION.
Is the multiplying any number with itself, and that pro-
duct 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
the index, or exponent of that power.'

EXAMPLES
What is the 5th power of 8.

8 the root or 1st power,

to

LINE

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32768 * 5th power, or sursolid. Ans.

What is the square of 17,1?
What is the square of ,085 ?
What is the cube of 25,4 ?
What is the biquadrate of 12?
What is the square of 71? .

Ans. 292,41 Ans. ,007225 Ans. 16387,064 3. Ans. 20736

Ans. 52

All

EVOLUTION, OR EXTRACTION OF ROOTS. WHEN the root of any power is required, the business of finding it is called the Extraction of the Root.

The root is that number, which by a continual multipli. cation into itself, produces to 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 root to any assigned degree of exactness.

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

1 Table of the Squares and Cubes of the nine digits. Kloots. 4112131415161718 1 97 Squares. 141 9 | 16 | 25 | 36 | 49 | 64 81 | Cubes. 111.81 27 | 64 | 125 | 216 343 512 1729

EXTRACTION OF THE SQUARE ROOT. Any number multiplied into itself produces a square. : ; To extract the square root, is only to find a number, which being multiplied into itself, shåll 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,

another over the place of hundreds, and so on; and if there are decimals, point them in the same manner, from units towards the right handl; which points show the number of figures the root will consist of..

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

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