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Case VIII. When the principal, time and amount are given, to find the rate per cent.

RULE 1. As the principal is to the interest for the whole time, so is 100 to its interest for the same time.

2. Divide the interest thus found by the given time ; the quotient will be the rate per cent.

EXAMPLES. 1. At what rate per cent. per annum, will 500 dole.. amount to $725 in 9 years.

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years 9)45 Interest of 100 dols. for 9 years.

Ans. 5 per cent.

2. At what rate per cent. per annum, will £620, amount to £793 12 in 7 years

?

Ans. 4 per cent. 3. At what rate per cent. per annum, will 420 dols. amount to $520,80, in 8 years ? Ans. 3 per cent.

CASE IX. When the principal, rate and amount are given, to find the time.

Rule. As the interest of the principal for 1 year is to one year, so is the whole interest to the time or number of years required.

EXAMPLES 1. In what time will 500 dols, amount to 725 dols. at 5 per cent. per annum ?

600
5

725 Amount.
25100

500 Principal. 1 year's

25 : 1 :: 225 whole interest. interest,

1

25)225(9 years, Ans.

225

NOTE. This case and Case VIII, prove each other.

2. In what time will £ 620, amount 10 £793 12, at 4 per cent per annum ?

Ans. 7 years. 3. In what time will 420 dols. amount to $520,80

Ans. 8 years. et 3 per cent per annum ?

4. In what time will 2500 dols. amount to 5200 dols. at 6 per cent. per annum ?

Ans. 18 years.

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Miscellaneous Questions to exercise the fore

going Cases.

1. What is the interest of dols. 936,28, for a year, at 4 per cent. per annum ?

Ans. dols. 37,45,118. 2. What is the intervist of dols. 371,85, for a year, at 5 per cent. per annum).

Ans. dols. 18,59,24 3. What is the interest of dols. 36,26, for 4 years, 11 months, and 6 days, at 5. per cent. per annum ?

Ans. dols. 9.39,1 34 4. What is the interest of dols. 561,29 for 9 weeks, at 41 per cent, per annum ?

Ans. dols. 4,37,1+ 5. What principal being put to interest 9 years, at 6 per cent. per annum, will amount to 770 dols. ?

Ans. 500 dols, 6. At what rate per cent will 500 dols. amount to 770 dols. in 9 years ?

Ans. 6 per cent. • 7. In what time will 500 dols. amount to 770 dols. at 6 per cent. per annum ?

8. In what time will 1 cent amount to 600 dols. at 6 per cent. per annum ?

Ans. 10000 years.

Ans. 9 years.

9. A gentleman had a daughter married on the day she was 18 years old, to whom he gave a note dated on the day she was born, and amounted then to 5200 dols. at 6 per cent. per annum, how much was the principal ?

Ans. 2500 dols. 10. What is the amount of a cent, for 1809 years, at 6 per cent. per annum ?

Ans. dols. 108,55.

COMPOUND INTEREST.

Compound Interest is an allowance for the forbearance of the principal and interest taken together, i.e. when the interest is not paid at the stipulated time, it is added to the principal, and their sum becomes a new principal, &c.

To find the compound interest of a sum for several years.

Rule. Calculate the interest for 1 year, as in the first case of Simple Interest ; add this interest and its principal together, which is the principal for the second year; calculate its interest as above, 2 and add this interest, to its principal, their sum will be the principal for the third year.

Go through as many such calculations as there are year's interest required ; add the last interest found to its principal, their sum will be the whole amount of principal and interest ; from the amount subtract the first principal given, the difference will be the whole interest required.

EXAMPLES

| What is the amount of £736 11 6, for 3 years, at 6 per cent. per annum, Compound Interest?

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2. Required the compound interest of dols. 725,50, for 2 years, at 6 per cent. per annum.

$725,50 principal for 1st. year.

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Ans. $89,67,1,8 Compound Interest for 2 years. 3. What is the compound interest of 680 dols. for 4 years, at 6 per cent. per annum ? Ans. $178,48,3.

4. What is the compound interest of dols. 637,25, for 5 years, at 5 per cent. per annum?

Ans. 176,06. 5. What is the amount of dols. 597,75 for 20 years, at 6 per cent. per annum, compound interest ?

Ans. dols. 1917,07,7. 6. What will 1350 dols. amount to in 3 years, at 5 per cent. per annum, compound interest?

Ans. dols. 1562,79,3.

BARTER.

Barter is the exchanging one kind of goods for another without loss or gain to either party ; questions in this rule are solved by finding what quantity of one kind of goods, at a given price, is equal in value to a given quantity of another kind, the price of the latter also being given.

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