3. $800.

Bradford, July 4, 1842.

For value received, I promise to pay Leonard Johnson, or order, on demand, eight hundred dollars, with interest.

Attest, Enoch True.

Samuel Neverpay.

On this note are the following indorsements :

Aug. 10, 1842, received one hundred forty-four dollars.

Nov. 1, 1842, received ninety dollars.

Jan. 1, 1843, received four hundred dollars.
March 4, 1843, received one hundred dollars.

What remains due June 1, 1843?

Ans. $88.02.

ART. 204. In the United States court, and in most of the courts of the several States, the following rule is adopted for computing the interest on notes and bonds, when partial payments have been made.

RULE. Compute the interest on the principal sum, from the time when the interest commenced to the time when the first payment was made which exceeds, either alone or in conjunction with the preceding payments, 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 and subtract the interest, as upon the first principal, and proceed in the same manner to the time of judg

ment.

This rule is illustrated in the following question.

Ex. 1. $ 365.50.

Lynn, Jan. 1, 1842. For value received, I promise to pay John Dow, or order, on demand, three hundred sixty-five dollars fifty cents, with in

terest.

Attest, Samuel Webster.

On this note are the following indorsements:
June 10, 1842, received fifty dollars.
Dec. 8, 1842, received thirty dollars.
Sept. 25, 1843, received sixty dollars.
July 4, 1844, received ninety dollars.
Aug. 1, 1845, received ten dollars.

Dec. 2, 1845, received one hundred dollars.

John Smith.

QUESTIONS. Art. 204. What is the rule generally adopted by the several States for computing the interest on notes and bonds, when partial payments have been made?

What remains due Jan. 7, 1847 ?

OPERATION.

Principal carrying interest from Jan. 1, 1842, to June 10, 1842,

Interest from Jan. 1, 1842, to June 10, 1842, (5 months,

9 days,)

Ans. $92.53.

$ 365.50

9.68

Amount, 375.18

First payment, June 10, 1842,

50.00

Balance for new principal,

325.18

Interest from June 10, 1842, to Dec. 8, 1842, (5 months,

28 days,)

9.64

Amount, 334.82

Second payment, Dec. 8, 1842,

30.00

Balance for new principal,

304.82

Interest from Dec. 8, 1842, to Sept. 25, 1843, (9 months,

Interest from Sept. 25, 1843, to July 4, 1844, (9 months,

Interest from July 4, 1844, to Dec. 2, 1845, (16 months, 28 days,)

Fifth payment, Aug. 1, 1845, (a sum less than

Sixth payment, Dec. 2, 1845, (a sum greater than the interest,)

$10.00

Interest from Dec. 2, 1845, to Jan. 7, 1847, (13 months,

5.71

$92.53

2. $1666.

Newburyport, June 5, 1838.

For value received, I promise to pay John Boardman, or order, on demand, one thousand six hundred sixty-six dollars, with interest. John J. Fortune.

Attest, T. Webster.

On this note are the following indorsements :July 4, 1839, received one hundred dollars.

Jan. 1, 1840, received ten dollars.

July 4, 1840, received fifteen dollars.

Jan. 1, 1841, received five hundred dollars.

Feb. 7, 1842, received six hundred fifty-six dollars.
What is due Jan. 1, 1843?

3. $960.

Ans. $767.08.

Newark, N. J., Oct. 23, 1840.

On demand, I promise to pay S. S. St. John, or order, nine hundred sixty dollars, for value received, with interest at seven per cent. John Q. Smith.

Attest, H. F. Wilcox.

On this note are the following indorsements :
Sept. 25, 1841, received one hundred forty dollars.
July 7, 1842, received eighty dollars.

Dec. 9, 1842, received seventy dollars.
Nov. 8, 1843, received one hundred dollars.

What is due Qct. 23, 1844?

4. $1000.

Ans. $807.76.

New York, January 1, 1839.

Two months after date, I promise to pay S. Durand, or order, one thousand dollars, for value received, with interest after, at seven per cent.

Attest, William S. Hall.

Paul Sampson, Jr.

On this note are the following indorsements: March 1, 1840, received one hundred dollars. Sept. 25, 1841, received two hundred dollars. Oct. 9, 1842, received one hundred fifty dollars. July 4, 1843, received twenty dollars.

Oct. 9, 1843, received three hundred dollars.

What is due Dec. 1, 1844?

Ans. $567.49.

PROBLEMS IN INTEREST.

ART. 205. A PROBLEM in arithmetic is a question, or proposition, which requires some unknown truth to be investigated.

ART. 206. In the preceding questions in interest, five terms or things have been mentioned; viz. the Interest, Amount, Rate per cent., Time, and Principal. The investigation of these involves five problems: I. to find the interest; II to find the amount; III. to find the rate per cent.; IV. to find the time; V. to find the principal.

With one exception, any three of the preceding terms being given, a fourth may be found by the rules deduced from the solution of the problems. But if the rate per cent., time, and amount are given, an additional rule is necessary to find the principal, which will form a sixth problem; but from its connection with Discount, its solution will be deferred until that subject is considered.

The Problems I. and II. have already been examined, and we now proceed to an examination of those remaining.

ART. 207. Problem III. To find the rate per cent., the principal, interest, and time being given.

Ex. 1. The interest of $300 for 2 years is $48; what is the rate per cent. ?

OPERATION.

$300

.02

$6.00) 4 8.00 (8 per cent.
4 8.0 0

Ans. 8 per cent.

We find the interest on the principal for 2 years at 1 per cent., and divide the given interest by it.

Since the interest of $1 at 1 per cent. for 2 years is 2 cents, the interest of $300 will be 300 times as much, equal to $6. Now if $6 is 1 per cent., $48 will be as many per cent. as $6 is contained times in $48, which gives 8 per cent. for the answer.

RULE. Divide the given interest by the interest of the given sum at 1 per cent. for the given time, and the quotient will be the rate per cent. required.

QUESTIONS. Art. 205. What is a problem in arithmetic? - Art. 206. How many terms or things have been given in the preceding questions in interest? Name them. What does an investigation of these terms involve? Name them. How many terms are given in each problem in order to find a fourth? What two problems have been examined?-Art. 207. What is Problem III.? Explain the operation. What is the rule for finding the rate per cent., the principal, interest, and time being given?

EXAMPLES FOR PRACTICE.

2. The interest of $250 for 1 year, 3 months, is $28.125; what is the rate per cent.?

3. If I pay $8.82 for the use of $72 for 1 year, 9 months, what is the rate per cent. ?

4. A note of $ 500, being on interest 2 years, 6 months, amounted to $550; what was the rate per cent. ?

ART. 208. Problem IV. To find the time, the principal, interest, and rate per cent. being given.

Ex. 1. For how long a time must $300 be on interest at 6 per cent. to gain $ 36?

OPERATION.

$300
.06

$18.00) 36.00 (2 years.

3 6.00

Ans. 2 years.

We find the interest on the given principal for 1 year, by which we divide the given in

terest.

Since the interest of $1 for 1 year is 6 cents, the interest of $300 will be 300 times as much, equal to $18. Now, if it require 1 year for the given principal to gain $18, it will require as many years to gain $36 as $18 is contained times in $36. Thus, $36 $182 years for the answer.

RULE.

Divide the given interest by the interest of the given principal for 1 year, and the quotient is the time.

EXAMPLES FOR PRACTICE.

2. If the interest of $140 at 6 per cent. is $42, for how long a time was it on interest?

3. How long a time must $ 165 be on interest at 6 per cent. to gain $14.85?

4. How long must $98 be on interest at 8 per cent. to gain $25.48 ?

5. A note of $ 680 being on interest at 4 per cent. amounted to $727.60; how long was it on interest?

QUESTIONS. Art. 208. What is Problem IV.? Explain the operation. What is the rule for finding the time, the principal, interest, and rate per cent. being given?