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simple in TEREST BY DECIMALS- 103

1067,50 amount. [Brought up. 200,00 first payment deducted.

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

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

438,345 balance due June 29, 1799.
25.30 interest for one year.

464,645 amount for one year.
269,750 amount of third payment for 74 months."

194,895 balance due June 29, 1800. mo, da. 5,6-7 interest to December 24, 1800. 5 2.5

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

* tablished by the Courts of Law in Massachusetts for computing interest on notes, yo. on which partial payments have been endorsed.

Compute the interest on the principal sum, from the tin-3 when the interest commenced to the first time when a polyment 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 subtract the payment made at that time, together with the preceding payments (if any) and the remainder forms a new principal; on which compute ard subtract the payments as upon the first principal, and proceed in this manner to the time of final settlement.”

* -t-. *250,00third payment with its interest from the time it was paid, up to 9.75 the end of the year, or from Nov. 14, 1799, to June 29, o which is 7 and 1-2 months.

-59.75 amount.

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104 81MPLE INTEREST by DECIMALs.

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, $200 2d payment June 29, 1799, 500 3d payment November 14, 1799, 260 How much remains due on said note the 24th of Decem ber, 1800? & cits. Principal, January 4, 1797, 1000,00 Interest to February 19, 1798, (134 mo.) 67,50

Amount, 1067,50

Paid February 19, 1798, 200,00 Remainder for a new principal, S67,50 Interest to June 29, 1799, (16; no.) 70,84

Amount, 938,34 Paid June 29, 1799, 500,00 Remains for a new principal, 45so Interest to November 14, 1799, (4 mo.) 9,86

Amount, 448,20 November 14, 1799, paid 200,00 Remains for a new principal, - 188,20 Interest to December 24, 1800, (13 mo.) 12,70 Balance due on said note, Dec. 24, 1800, 20090

& cos.

The balance by Rule 1, 200,579
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 payments

endorsed upon it as follows, viz. 8 ros. 1st payment May 1, 1800, 40,00 2d payment November 14, 1800 8,00

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3d payment April 1, 1801, 12,00 4th payment May 1, 1801, 30,00 How much remains due on said note the 16th of Sep to mber, 1801 : 8 cos. 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

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, (44 mo.) 10,92

Balance due on the note, Sept. 16, 1801, $455,57

so-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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166 - invol. UTION.

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

400x1,06 x 1,06x1,06 x 1,06=E504,99-Ho

[E504 19s. 9d. 2,754rs.--Ans.

The same by Table 1.

Tabular amount of £1=1,26247
Multiply by the principal 400

Whole amount=#E504,988.00 2. Required the amount of 425 dols. 75 cts. for 3 years, at 6 per cent compound interest? Ans. $507,74 cts. + 3. What is the compound interest of 555 dols for 1years at 5 per cent.” By Table I. Ans. 543,85 cts. + 4. What will 50 dollars amount to in 20 years, at 6 per cent compound interest? Ans. $160, 35 cts. Gom.

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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--OLUTION OR EXTRACTION O-Roc-T-- 167

what is the square of 17,11 Ans. 292,41 What is the square of,0852 Ans. ,0072:25 What is the cuba of 25,47 Ans. 16387,064 What is the hiquadrate of 12? Ans. 20736 What is the square of 71 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 continued multipli cation 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 uly assigned degree of exactness. The roots which approximate are called surd roots, and hose which are perfectly accurate are called rational roots.

A Table of the Squares and Cubes of the nine digits.

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Co. III's 137 IGITT2531513.131513 To
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 o

there are decimals, point them in the same manner, from
units towards the right hand; which points show the num-
ber of figures the root will consist of
2. Find the greatest square number in the first, or left
mand period, place the root of it at the right hand of the

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