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THE SAME QUESTION.

Principal 800 dollars, and four years interest 192 dollars.

Whole amount, up to 1st Jan. 1827 $ 992 00 Paid 1st July, 1823

$100 Interest thereon to 1st Jan. 1827 21

amount $121 Paid 1st Nov. 1823

150 Interest thereon to 1st Jan. 1827 28 50

178 50 Paid 1st Jan. 1824

100 Interest to 1st Jan. 1827

18

118 Paid 1st Sept. 1824

80 Interest to ist Jan. 1827

11 20

9120 Paid 1st Sept. 1825

100 Interest to ist Jan. 1827

108 Paid 1st April, 1826

150 Interest to 1st Jan. 1827

6 75

156 75

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RULE 7. When payments are made in shorter periods than a year, that is, in 4, 6, 7, 8 months, &c. from each other, find the interest on the principal sum for one year, add it to the principal, and compute the interest on the sum paid, from the time it was paid, up to the end of the year, add it to the sum paid, and deduct it from the principal and interest, added as above. If any payment be made of a less sun than the interest due at the time of such payment, no interest is to be calculated, but only on the principal sum, for any period.

THE SAME QUESTION.

amount $ 848 00

1st Jan. 1823, principal sum

$800 One year's interest, to 1st Jan. 1824 48 Paid 1st July, 1823

100 Six months interest, to 1st Jan. 1824 3 Paid 1st Nov. 1823

150 Interest to 1st. Jan. 1824, (2 months)

1 Paid 1st Jan. 1824

103

50

50

151 100

354 50

New principal 493 50

New principal brought over $49350 One year's interest on 493 dolls. 50 cts. to 1st Jan. 1825 29 61

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New principal 441 51 One year's interest on 441 dolls. 51 cts. to 1st Jan. 1826 26 49

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Another method. RULE 8. 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, the days in a year, and you will have the whole interest due, &c.

THE SAME QUESTION.

By the second rule, the sum of the several balances, multiplied into the number of days they were at interest, is

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Different methods.
By Rule 1, due on said note, 8 232 80+
Rule 2,

219 84 Rule 8,

218 46 Rule 4,

218 48

By Rule 5, due on said note, 8218 55
Rule 6,

218 55
Rule 7,

231 21 Rule 8,

218 48 NOTE. I have here given eight examples, by which interest on notes, where partial payments are made, is onmputed. The first rule is most in use, and is allowed to be the most just; yet there is a great difference between it and all the rest, save the seventh.

I cannot inform the scholar, whether there is or not in this state, a rule established by law for calculating interest on bonds, notes, &c. where partial pagments are made; but in some of the New England states there is..

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COMPOUND INTEREST Is when the interest is added to the principal for one, or at the end of a year, and that sum becomes a new principal for another year, and the interest thereof added again, &c. for any number of years. This is called Compound, or interest

upon

interest. RULE 1. Find the interest for one year, and add it to the principal, which is the amount for one year. Find the interest of that amount, which add as before, for the amount of the second year, and so on for any number of years. Subtract the original principal from the last amount, and the remainder will be the compound interest for the whole time.

Rule 2, by the table. Multiply the figures standing against the number of years by the given principal, and the product is the amount required, from which, if you subtract the principal, the remainder is the compound interest.

RULE 3, by the table. Multiply the given principal continually by the amount of one dollar for one year, at the rate per cent, given, until the number of multiplications is equal to the given number of years, and the product will be the amount required, from which, if you subtract the given principal, the remainder will be the compound interest.

Yrs.[5 per cent.16 per cent. Yrs. 5 per cent.6 per cent.
1,05000 1,06000

1,71034 1,89829 1,10250 1,12360

1,79585

2,01219 1,15762 1,19101

1,88565 2,13292 $1,21550

1,26247 1,97993 2,26090 1,27628 1,33822 2,07893 2,39655 1,34099 1,41851 2,18287 2,54727 1,40710 1,50.363 2,29201 2,69277 1,47745 1,59384 2,40661 2,85433 1,55132 1,68947 2,52695 3,02559 1,62889 1,79084

2,65329 3,20713

5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

By this table, compound interest may be more expeditiously calculated, in which the amount of one dollar for any number of years, not exceeding. 20, is shewn, at 5 and 6

per cento per annum, compound interest. Look in the left-hand column for the given nuinber of years, and run your eye along towards the right hand, under 5 or 6 per cent. (as the question demands, and you will find the number sought.

1. How much is the compound interest of 200 dollars for 4 years, at 6 per cento per annum?

$ 200 Ist principal

6

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answer

252,49,53,92 amount for 4 year's
200

principal
$ 52,49,53,92

Operation by Rule 2. Tabular number for 4 years, at 6 per cent. 1,26247

200

Amount 252,49,4,00
Principal 200

Answer $ 52,49,4
Operation by Rule 3.
'Tabular number for 1 year, 1,06000=1,06
Then 200 X 1,06 X 1,06 X 1,06 X 1,0658252,49,5+

Deduct the principal 200

Ans. % 52,49,5

2. How much is the amount of 500 dollars for 3 years, at 6 per cent. per annum, compound interest ?

'Ans. 595 dollars 50+ cents. 3. Required the compound interest of 100 dollars for 3 years, at 6 per cent. per annum?

Ans. 19 dollars 10+ cents. 4. What is the amount of 750 dollars for 4 years, at 6 pes cent. per annum, compound interest ?

Ans. 946 dollars 85 + cents. 5. How much will 650 dollars amount to in 20 years, at 6 per cent. per annum, compound interest ?

Ans, 2084 dollars 63 + cents. 6. What is the compound interest of 100 dollars for 11 years, at 6 per cent. per annum ?

Ans. 89 dollars 82 cents 9 mills. 7. What is the amount of 425 dollars 75 cents for 3 yrs: at 6 per cent. per annum, compound interest ?

Ans. 507 dollars 7+ cents. 8. How much is the amount of 300 dollars for 4 years, at 5 per cent. per annum, compound interest.

Ans. 364 dollars 65 cents. 9. A father left 6000 dollars at compound interest, at 6

per cent. per annum, to be equally divided among three sons, when the youngest, who was 12 years

should arrive at 21. What will be each son's share then ?

Ans. 3378 dollars 94 cents each. Nork. The ratio is the simple interest of one dollar for one year, at any proposed rate per cent, and is thus found.

As 100

5 :: 1 to 0,05 ratio. As 100 : 6 :: 1 to 0,96 ratio. The table is constructed in the following manner. To find the tabalar numbers, say,

As 100 : 105 :: 1 to 1,05 = 1,05000 tabular number.

As 100 : 106 :: 1 to 1,06 = 1,06000 tabular number. If the pupil does not wish to work by the tabular numbers, he must make a stating for every year in the question, as in simple interest.

of age,

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COMMISSION, INSURANCE & BROKERAGE.

Commission is an allowance of so much per cent. to a correspondent, for buying and selling goods for his employer, and is performed the same as interest for a year.

Rule. Multiply the given sum by the rate per cent. and divide the product by 10); or cut off two figures to the right hand, and all to the left will be dollars..

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