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29. What is the interest of £129 7s. 3d. 3qrs., for 3 years, 7 months and 5 days? Ans., £27 18s. 41⁄2d. 30. What is the amount of £320 10s. 6d., on interest for 2 years, 6 months and 15 days? Ans.,£369 8s. 1 d. 31. What is the amount of £430 7s. 8d. 3qrs., for 4 years, 3 months and 20 days? Ans., £111 3s. 7d. 3qrs. When the rate of interest is any other than six per cent., and the time consists of years, months and days,

Find the interest first for 6 per cent., and then for 1 per cent., and multiply the interest at 1 per cent. by the given rate, and the product will be the answer.

EXAMPLES.

32. What is the interest of $680 for 1 year and 6 months, at 7 per cent.?

Answer, $71,40.

Operation.
$680

,09

6)61,20 interest at 6 per cent.

10,20 interest at 1 per cent.
7

$71,40 interest at 7 per cent.

33. What is the interest of $336,40 for 2 years, S months and 3 days, at 3 per cent.? Ans., $26,996. 34. What is the interest of $556,36 for 3 years, at 1 per cent.? Answer, $16,69.

NOTE. The interest of any sum at I per cent. for 1 year, is the principal itself, with the separatrix moved two figures further towards the left; therefore, to obtain the interest at 1 per cent. for any number of years, we have only to multiply by the number of years.

35. What is the interest of $0,56 cents for 5 years, 5 months and 10 days, at 9 per cent.? Ans., $,276.

36. What is the amount of $1000, on interest for 5 years Answer, $418,16.

7 months, at 7 per cent? 37. What is the interest of $1569,20 for 1 year, at 1 Answer, $15,692.

per cent.?

QUESTIONS. 15. Rule, when the rate of interest is any other than 6 per cent.? 16. What is the interest of any sum for 1 year at 1 per cent.?

INTEREST BY CANCELLING.

RULE.

State the question as in Direct Proportion, by placing the terms of demand on the right, and the terms of supposition on the left.

EXAMPLES.

1. What is the interest of $500 for 3 years, at 6 per cent.?

NOTE I. The terms of supposition in Interest, are not expressed, being always 100 and 1 year. The foregoing question may be expressed thus:

What is the interest of $500 for 3 years, if the interest of $100 for 1 year be $6?

Operation.

What interest. 500 $

If $1003 years.
Year 16 $

$90 Answer.

2 What is the interest of $720 for 1 year and 6 months, at 6 per cent. ?

Answer, $64,80.

NOTE II. When the given time is months, weeks, or days, either less or greater than a year, reduce it to the lowest denomination, and 1 year, the time in the supposition, to the same denomination.

Answer, $70,40.

3. What is the interest of $642,255 for 2 years and 6 months? Answer, $96,338. 4. What is the interest of $1000,68 for 2 months and 15 days? Answer, $12,508. 5. What is the interest of $440 for 4 years, at 4 per cent.? 6. What is the interest of $60,10 for 5 years, at 5 per cent? Answer, $15,025. 7. What is the interest of $160 for 36 days, at 7 per cent.? Answer, $1,12. 8. What is the amount of $780 for 3 years and 4 months, at 3 per cent.? Answer, $858.

NOTE III. If we multiply the amount of $1 for the given time, by the given principal, the result will be the same as adding the principal to the interest. Thus the amount of $1 for 3 years and 4 months, at 3 per cent., is $1,10, which multiplied by $780, gives $858, the answer.

I. When time, rate and amount are given, to find the prin

cipal.

1. What principal will amount to $858 in 3 years and 4 months, at 3 per cent. ?

The student will perceive, that this question is the reverse of question 8th, preceding, and also, that 858 is there a product, of which 1,10, the amount of $1 for the given time, is a factor; therefore, if we divide 858 by 1,10, we shall obtain the other factor, or the principal required— 858÷1,10=$780, the answer. Hence the

RULE.

DIVIDE the given amount by the amount of $1 for the given time, and the quotient will be the answer.

EXAMPLES.

2. What principal will amount to $778,10, in 4 years and 3 months, at 6 per cent.? Answer, $620. 3. What principal will amount to $650, in 6 years, at 5 per cent.?

Operation by Cancelling.

What principal.[650$ amount.
Amount, $1,30| 1$ principal.

$500 Answer.

4. What principal will amount to $738,40, in 7 years?

Answer, $520.

II. When time, rate and interest are given, to find the

principal.

1. What principal will gain $27,52, in 1 year,5 months and 6 days?

We have seen, that the interest of a given principal for a given time, is the product of the interest of $1 for the same length of time, and the principal; therefore, if we divide $27,52 by ,08,6, the interest of $1 for the given time, we shall obtain the principal required, as before.— Hence the RULE :

DIVIDE the given interest by the interest of $1 for the given time, and the quotient will be the answer. 2. What principal will gain $19 in 4 months, at 6 per Answer, $950.

cent. ?

3. What principal will gain $1500 in 5 years, at 6 per cent. ? Answer, $5000.

III. When principal, interest and time are given, to find the rate per cent.

1. If $50, in 6 months, gain $1,50, what is the rate per cent. ?

If the interest of $50, at 1 per cent., be 25 cents, then the quotient of $1,50, the whole interest, divided by 25 cents, will be the rate per cent. required. 1,50÷25=6 per cent., answer. Hence the RULE:

DIVIDE the given interest by the interest on the given principal, at 1 per cent. for the given time, and the quotient will be the answer.

2. If $300 gain $12 in 8 months, what is the rate per

cent.?

Operation by Cancelling.

What interest. |100 $

If $300 12 m.

m. 8 12 int.

Answer, 6 per cent.

3. If $740 gain $27,75 in 9 months, what is the rate per cent. ? Answer, 5 per cent.

4. If $1000 gain $75 in 6 months, what is the rate per

cent.?

Answer, 15 per cent.

IV. When principal, rate and interest are given, to find

the time.

1. In what time will $300 gain $12, at 6 per cent.

Operation.

In what time. 12$ Int.

Int. $18 1 year.

Having found the interest of $300 for 1 year, the question may be expressed thus: In what time will $12 interest be gained, if $18 be gained in 1 year? It is evident, that the ratio of the interest for 1 year is to the given interest as 1 year is to the time required. Hence the RULE :

32 8 months.

DIVIDE the given interest by the interest of the given principal for 1 year, and the quotient will be the answer. 2. In what time will $240 gain $4,80, at 6 per cent? Answer, 4 months. $600 amount to $645, at 5 per Answer, 1 year and 6 months.

3. In what time will cent.?

4. In what time will $375 gain $28,123, at 6 per cent.? Answer, 1 year and 3 months.

5. The interest on a note of $225, at 4 per cent., was $11,40. What was the time?

Answer, 1 year, 3 months, 6 days.

To find the interest on notes, &c., when partial payments have been made.

The methods of computing interest on notes and bonds differ in different places; but the following is the more general method, and is established by law in Massachu

setts.

Compute the interest up to the time of the first payment; and if the payment exceed the interest, deduct the excess from the principal, and cast the interest on the remainder up to the second payment, and so on. If the payment be less than the interest, cast the interest up to the time when the sum of the payments shall exceed the interest; then deduct the excess from the principal, and proceed as before.

$3784,25.

1. For value received, I promise to pay JAMES LARNED, or order, three thousand, seven hundred, eighty-four dollars and twenty-five cents, with interest.

July 10, 1826.

JOHN FISHER.

On this note were the following endorsements:
Jan. 16, 1827, received $148,21

Aug. 11, 1827,

50,00

Dec. 24, 1828,

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Feb. 12, 1830,

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What was due Dec. 14, 1830 ? Answer, $464,867.

For Operation, see next page.

QUESTIONS. 17. Method of computing interest on notes, &e., established by law in Massachusetts?

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