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The same question by rule second.

$6.22 principal.

⚫06 rate.

6 mo.of a year. ).3732 1 year's interest.

2

•7464 2 year's interest.
•1866 6 month's interest.
0103† 10 day's interest.

Ans. 9433† interest for 2 yr.6 mo. 10ds.

2. What is the interest of $10.10 cts. for 10 years, 11 months, at 9 per cent. ?

years. mo. years.

c. m.

10 1110-916×10.10X 09 $9.92.2† Ans:

D. c.

The same question by rule second.

10.10

⚫09

of 6 mo. of 6

66

6 mo. of 1 year. ).9090 1 year's interest.

10

9.0900 10 yrs. interest.
)0.4545 6 months' interest.
0.2272+ 3 months' interest,
0.1515 2 months' interest.

]). c. m.

Ans. 9.92 31.

$9.9232+

3. What is the interest of $213.23 cts. for 3 years, 12 days, at 10 per cent. ? Ans. $64-67 cts. 9†m.

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The same question by rule second.

Ans. $64 67 cts. 9†m. 4. What is the interest of $23-23 cts for 1 year 9 mo. at 6 per cent. ? Ans. $2.43 cts. 9† m.

The same question by rule second,

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Ans. $2.43 cts. 9 m.

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5. What is the interest of $121.11 cts. for 2 years, mo. at 5 per cent. ? Ans. 15 64 cts. 3 m. The same question by rule second.

Ans. $15.64 cts. 3† m.

NOTE. In the preceding examples I have considered 30 days a month, and 12 months a year; which is the general method of casting interest; but by this method 5 days are lost in a year; 12x30360 days; which in large sums would amount to something worthy of notice.

CASE IV.

To cast interest for any number of days, allowing three. hundred sixtyfive days to a year.

RULE.-Reduce the given number of days to the dec imal of a year, which contains 365 days; then multiply the principal, rate, and time together, point off for deci mals according to the rule of decimal fractions, and the product is the answer.

Examples.

1. What is the interest of $21.20 cts. for 27 days, at 9 per cent. per annum?

27 days is 270739

$21.20 X 09 X 073914 cts. I tmill Ans. 2. What is the interest of $12.06, for 3 years 141 days at 6 per cent. per annum ? Ans. $2.45.

3. What is the interest of $3.03, for 136 days, at 6 per cent. per annum ? Ans, 06 cts. 7† m.

CASE V.

When the time is months, and the rate per cent. is six.

RULE-Multiply the principal by half the number of months, (which is just equal to the rate for the time when the annual rate per cent. is six) if the months are odd, annex 15 to the right hand, the product is the interest for the time.

Examples.

1. What is the interest of 21 dollars for 10 months, at 6 per cent. per annum?

)10 months 05×82181·05 cts. Ans. 2. What is the interest of 250 dollars 11 cents, for 16 months, at 6 per cent. per annum?

Ans. $20.00 cts. 8† m.

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3. What is the interest of $121.12 cents, for 21 months, at 6 per cent. per annum ?

Ans. $12.71 cts. 7 m. 4. What is the interest of 9 dollars, 9 cents, for 9 months, at 6 per cent. per annum?

Ans. 40 cts. 9† m.

CASE VI.

When the time is mo ths, and the rate any other than six,

RULE. Find the rate for the time by proportion; say, as twelve months is to the rate per annum, so is the given number of months to the rate for the time.

Examples.

1. What is the interest of $26.21 cts. for 8 months, at 9 per cent. per annum ?

Months. Per cent. Months.

As 12 : 9 : : 8 : 6 the rate for that time. $26.21 × 06 rate $1.57·2 Ans.

2. What is the interest of $12.11 cts. for 21 months, at 11 per cent. per annum? Ans. $2.33-1† m.

3. What is the interest of 111 dols. for 13 months at ten per cent. per annum ? Ans. $12.02.5

4. What is the interest of $19 for 22 months, at 12 per cent. per annum? Ans. $4.18 cts.

CASE VII.

When endorsements are made on notes, &c.

RULE 1. Find the amount of the note to the end of the first year; and find also the amount of all the endorsements (made in that year,) and subtract the amount of the endorsements from the amount of the note, the remainder will be a principal for the second year; thus proceed from year to year; the last principal thus found will be what is due on final settlement by this method the endorsements are applied to keep down the interest.

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RULE 2. By a statute of Massachusetts, the following rule is established to cast interest upon secu. rities, where endorsements have been made, viz. find the interest upon the note to the time of the first payment, and add it to the principal; and from the sum subtract the payment at that time made; if the endorsement is not equal to the interest at that time due, the interest is cast to the next endorsement, and the two endorsements are added together, and their sum is subtracted; the remainder forms a new principal, interest on which must be cast to the next endorsement, &c. the next endorsement must be taken therefrom; and thus proceed through the whole.

Examples by rule first.

1. Mr. Jenkins borrowed $1000 of Mr Thorn dike, and promised to pay it to him in one year, with lawful interest; but in six months after he payed $500; I demand what was due at the end of the year.

$1000 in 1 yr. amounts to $1060 amt. of note. $500 in 6 mo. amounts to 515 amt. of endor.

Ans. $545 due.

The same question by rule second.

$1000 in 6 mo. amounts to $1030.00 cts.
endorsement subtracted 500.00

a new principal $530:00

$530.00 cts: in 6 mo. more amts. to $545.90 cts. due on settlement; 90 cts. more than by rule first.

Example second, by rule first.

2. S. K. GILMAN borrowed $20000.00 cts. of D. S. LEAVITT, and promised to refund the same in one year with simple interest; but it so happened

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that he paid $5000 of it in 3 months which was en-
dorsed, and at the end of the year he paid the re-
mainder; what was due on settlement?

Amount of $20000.00 in one year $21200.00
Amount of endorsement in 9 mo. 5225.00

due on settlement. Ans. 815975.00
The same question done by rule second.
Amount of $20000 in 3 months. $20300.00
endorsements subtracted 5000.00

new principal 815300.00

Amount of new principal in 9 mo. 15988.50
$13.50 cts. more than by rule first.

NOTE I.-The reader will observe that the two methods do not agree, and the reason is obvious: in the first example by rule first, Mr. Jenkins pays Mr. Thorndike 500 dollars, six months before his note was due, and on settlement Mr. Jenkins charges Mr. Thorndike with the use of 500 dollars, six months, in addition to the sum then paid; (and I conceive it just and right, for he might have put the 500 dollars to use, to some other person, and not have paid Mr. Thorndike till his note was due; and then he certainly would have had the amount of 500 dollars to have met Mr Thorndike's demand, viz. 515,) and Mr. Thorndike would have demanded of bim 1000 dollars, and one year's interest; viz. $1060-515-545 due on settlement, same as by method first.

NOTE II.-By rule second the interest of 1000 dollars is found for the first six mo, and added to the principal, and then the 500 dollars is subtracted; and interest is cast on the remainder for the remaining six months; thus it is obvious that the 30 dollars interest, that was added at the expiration of the first six months, absolutely became a part of the prnicipal and carried interest the remaining six months; and of course makes the difference in the two methods.

$30 X 06x 6 months 90 cents the difference as before. NOTE III.-In the second question you will see that the difference in the two methods is 13 dols. 50 cents; and it is the. interest of the 300 dollars interest, which was added at the expiration of the first three months; which of course became a part of the principal, and bore interest the remaining nine months.

$300×·06×9 months $13.50.

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