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When interest is to be calculated on cash accounts, &c. where partial payments are made; multiply the several balances into the days they are at interest, then multiply the sum of these products by the rate on the dollar, and divide the last product by 365, and you will have the whole interest due on the account, &c.

EXAMPLES.

Lent Peter Trusty, per bill on demand, dated 1st of June, 1800, 2000 dollars, of which I received back the 19th of August, 400 dollars; on the 15th of October, 600 dollars; on the 11th of December, 400 dollars; on the 17th of February, 1801, 200 dollars; and on the 1st of June, 400 dollars; how much interest is due on the bill, reckoning at 6 per cent. ?

1800,

June 1, Principal per bill,
August 19, Received in part,

dolls. days. products.

2000

79 | 158000

400

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Jane 1, Ret'd in full of principal, 400

388600

.Then 388600

,06 Ratio.

$cts. m.

365)23316,00(65,879 Ans. = 63 87 9+ The following Rule for computing interest on any note, or obligation, when there are payments in part, or endorsements, was established by the Superior Court of the State of Connecticut, in 1784.

RULE.

"Compute the interest to the time of the first pay

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Let the foregoing example be solved by 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.

3d payment November 14, 1799.

$200

500

260

How much remains due on said note the 24th of De

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Remains for a new principal,

438,34

Interest to November 14, 1799, (4 mo.)

9,86

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

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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.

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$cts.

40,00

8,00

3d payment April 1, 1801.

4th payment May 1, 1801.

12,00

30,00

How much remains due on said note the 16th of Sep

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Paid May 1, 1800, a sum exceeding the interest, 40,00

New principal, May 1, 1800,
Interest to May 1, 1801, (1 year.)

467,50

28,05

Amount, 495,55

Paid Nov. 4, 1800, a sum less than the

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445,55

10,02

$455,57

New principal May 1, 1801,

Interest to Sep. 16, 1801, (4) mo.)

Balance due on the note, Sept. 16, 1801,

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

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EXAMPLES.

1. What will 400l. amount to in 4 years, at 6 per cent. per annum, compound interest?

400×1,06×1,06 × 1,06×1,06=£504,99+ or [504 19s. 9d. 2,75qrs.+ Ans. The same by Table I.

Tabular amount of £1=1,26247

Multiply by the principal

400

Whole amount=£504,98800

2. Required the amount of 425 dols. 75 cts. for 3 years, at 6 per cent. compound interest. Ans. $507,7cts.+ 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. 64m.

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 the index, or exponent of that power.

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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 7?

Ans. 292,41

Ans. ,007225 Ans. 16387,064 Ans. 20736

Ans. 52%

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 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 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.

A Table of the Squares and Cubes of the nine digits. Roots. 1|2|3| 4| 5 | 6 71 81 91 Squares. 1|4| 9|16| 25| 36| 49 | 64 81 Cubes.

|1|8|27| 64 | 125 | 216 | 343 | 512 | 729]

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, shall 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 hand; 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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