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If settlement is not made, till more than a year has elapsed after the commencement of interest, the preceding mode of computing interest, when partial payments have been made, ought not to be adopted; and indeed it is not in strict conformity with law.

The United States Court, and the Courts of the several States, in which decisions have been made and reported, with the exception of Connecticut and Vermont, and a slight variation in New Jersey, have established a general rule for the computation of interest, when partial payments have been made. This rule is well expressed in the New York Chancery Reports, in a case decided by chancellor Kent, and here given in the Chancellor's own words, as follows.

The rule for casting interest, when partial payments have been made, is to apply the payment, in the first place, to the discharge of the interest then due. If the payment exceeds the interest, the surplus goes towards discharging the principal, and the subsequent interest is to be computed on the balance of principal remaining due. If the payment be less than the interest, the surplus of interest must not be taken to augment the principal; but interest continues on the former principal until the period when the payments, taken together, exceed the interest due, and then the surplus is to be applied towards discharging the principal; and interest is to be computed on the balance, as aforesaid..

The interest on the following notes, must be computed by the above legal rule.

(116.) - Washington, March 4th. 1832.

For value received, I promise Nehemiah Adams to pay him or order the sum of one thousand two hundred dollars, on demand, with interest. Charles Train.

Attest. William Dorr.

The following endorsements were made on this note. June 10th. 1832, received one hundred and sixty-nine dollars and twenty cents. Oct. 22d. 1832, received twenty dollars. March 30th. 1833, received twenty-eight dollars. Nov. 5th. 1833, received six hundred and eighteen dollars and five cents. What was the balance due, on taking up this note, March 5th. 1834 ?

Principal,
Interest from Mar. 4, to June 10, (3 in. 6 d.),

First Amount,
First payment - - •. • -,
Balance, forming a new principal,
Interest from June 10, to Oct. 22, (4 m. 1
Second payment - -
Leaving interest unpaid, -
Interest from Oct. 22, to Mar. 30, (5 m. 8 d.),

$ 1200. - - 19.20 . 1219.20 - - 169.20

- 1050.00 $23.10 20.

3.10 27.65 30.75 28.00

2.75 37.80 40.55 - - 1090.55 - - 618.05 - - 472.50 - - 9.45 - - $ 481.95

Third payment, - - - - -
Leaving interest unpaid, - -
Interest from Mar. 30, to Nov. 5, (7 m. 6 d.),

Second Amount,
Fourth payment, - - - - -
Balance, forming a new principal, - -
Interest from Nov. 5, to Mar. 5, (4 m.), -
Balance due on taking up the note, - -

(117.)

Richmond, Jan. 5th. 1833. For value received, I promise Joseph Tufts to pay him or order one hundred and forty-three dollars and fifty cents, on demand, with interest. John Hanes.

Two payments were endorsed upon this note : viz. April 13in. 1833, received forty-five dollars and eighty-four cents. Dec. 22d. 1833, received fifty-four dollars and fifteen cents. The balance of this note was paid March 28th. 1834. How much was it?

(118.)

Raleigh, July 1st. 1832. For value received, I promise Charles Goodrich to pay him or order the sum of six hundred and twenty-five dollars and fifty cents, in three months, with interest afterward.

John Frink. Three payments were endorsed upon this note: viz. January 1st. 1833, received two hundred dollars. Nov. 1st. 1833, received twenty dollars. Jan. 1st. 1834, received three hundred dollars. The balance was paid May 1st. 1834. How much was it?

(119.)

Charleston, Dec. 22d 1830. For value received, I promised George Winship to pay him or order ninety-seven dollars and eighty cents, on demand, with interest,

Thomas White.

The endorsements made on this note were the following. Oct. 12th. 1831, received twelve dollars eighty-five cents. July 20th, 1832, received twelve dollars and seventeen cents. Feb. 26th. 1833, received fourteen dollars and ninety-five cents. August 26th, 1833, received thirty-six dollars and ten cents. Required the balance, which was paid Jan. 31st. 1834.

(120.)

Augusta, January 1st. 1331. For value received, I promise Israel Capen to pay him or order eighty-four dollars and forty cents, on demand, with interest.

Edward Ruggles. On the back of this note were the following endorsements. Oct. 9th. 1831, received nineteen dollars and thirty-two cents. July 15th. 1832, received twenty dollars. April 9th. 1833, received twenty-one dollars and eighty-one cents. Oct. 9th. 1833, received twenty-two dollars and fifteen cents. The balance of this note was paid Feb. 19th. 1834. How much was it?

(121)

New Orleans, Feb. 22d. 1830. For value received, I promise Maynard and Noyes to pay them or order the sum of nine hundred dollars, in three months, with interest till paid. Isaac Jettison.

Attest. William Proctor.

The following payments were endorsed upon the note. May 22d. 1830, received twenty-five dollars. Sept. 22d. 1830, received fifteen dollars. May 22d. 1831, received thirty-five dollars. May 22d. 1832, received one hundred and forty-five dollars and twelve cents. Dec. 4th. 1832, received one hundred and twenty-five dollars and sixty cents. May 22d. 1833, received two hundred and nineteen dollars and sixty cents. Dec. 31st. 1833, received two hundred and sixty-eight dollars and twenty-five cents. The balance of this note was paid Feb. 24th. 1834. What was the balance?

(122.)

Cincinnati, Dec. 1st. 1830. For value received, I promise Horatio Davis to pay him or order the sum of one thousand dollars, on demand, with interest till paid.

Edward Lang. Five partial payments were endorsed on this note: viz. Feb. 1st. 1832, received seventy-five dollars. June 1st. 1832, received twenty dollars. August 1st. 1833, received twenty dollars. October 1st. 1833, received seven hundred and fifty dollars. Feb. 1st. 1834, received one hundred dollars. The balance of this note was paid June 1st. 1834. How much was it?

(123.) : Louisville, April 4th. 1832.

For value received, I promise Samuel H. Wheeler to pay him or order the sum of three hundred and ninetysix dollars, on demand, with interest, at the rate of 7 per cent. a year, till paid.

George Guelph. Partial payments were made on this note, as follows: Sept. 14th. 1832, received twelve dollars. May 4th. 1833, received eighteen dollars. Oct. 24th 1833, received forty-nine dollars twelve cents. The balance was paid May 30th. 1834. What was the balance ?

(124.)

- Nashville, Sept. 7th. 1831. For value received, I promise Darius Pond to pay him or order the sum of four hundred and eighty-six dollars and ninety cents, on demand, with interest at the rate of 7 per cent. a year.

Martin Smith. The following partial payments were endorsed on this note. March 22d. 1832, received one hundred and twenty-five dollars. Nov. 29th. 1832, received one hundred and fifty dollars. May 13th. 1833, received one hundred and twenty dollars. The balance was paid April 19th. 1834. Required the balance.

(125.)

Albany, August 13th. 1930. For value received, I promise Theodore Leonard to pay him or order the sum of two hundred and ninetyeight dollars and nineteen cents, on demand, with interest at the rate of 7 per cent. a year. Stephen Kirkland.

Attest. W. Stevenson.

The following endorsements were made on this note. April 6th. 1831, received fifty-four dollars. Dec. 17th. 1831, received forty-two dollars. June, 21st. 1832 received sixty-one dollars. Feb. 26th. 1833, received thirty-seven dollars and eighty cents. July 8th. 1833, received seventy-five dollars. The balance was paid May 12th. 1834. How much was the balance ?

COMPOUND INTEREST. Compound interest is that which is paid not only for the use of the principal, but also, for the use of the interest after it becomes due.

When the interest is payable annually, find the interest for the first year, and add it to the principal, and this amount is the principal for the second year. Find the interest on this second principal, and add as before; this amount is the principal for the third year: and so on through the whole number of years. When the interest is payable half-yearly, or quarterly, find the interest for half a year, or a quarter of a year, and add it to the principal, and thus proceed through the whole time. Subtract the first principal from the last amount, and the remainder is the compound interest.

126. What is the compound interest of a thousand dollars for 3 years, at 6 per cent. per annum ? $ 1000. principal.

60. interest for the first year. 1060. amount, principal for the second year.

63.60 interest for the second year.
1123.60 second amount, principal for third year.

67.416 interest for the third year.
1191.016 third amount.
1000. first principal deducted.

$191.016 Answer. 127. What is the compound interest of 740 dollars for 6 years, at 6 per cent. per annum ?

128. What is the compound interest of 500 dollars, for 4 years, at 7 per cent. per annum ?

129.. To what sum will 450 dollars amount, in 5 years, at 5 per cent. per annum, compound interest ?

130. What is the compound interest of £760 10s. for 4 years, at 4 per cent. per annum ?

131. A gave B a note for 300 dollars, with interest at 6 per cent. a year, payable semiannually. How much did it amount to in 2 years, at compound interest ?

132. At compound interest, what will 600 dollars amount to in 11 year, at the rate of 6 per cent. a year, interest payable quarterly?

PROBLEMS IN INTEREST. In reviewing the subject of simple interest, we perceive four several problems, which arise from its conditions, and which we shall now distinctly notice.

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