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there were payments endorsed upon it as follows, viz. : April 20th, 1827, Rec'd. 300 dollars; May 15th, 1828, Received 200 dollars; what remained düe May 10th, 1829; interest at 7 per cent?

Ans. $191,90cts.

The following Rule was established by the Superiour Court of Connecticut, in 1784.

RULE II.--" Compute the interest to the time of the first payment, if that be one year or more from the time the interest commenced, add it to the principal, and deduct the payment from the sum total. It there be after payments made, compute the interest on the balance due to the next payment, and then deduct the payment as above; and in like manner from one payment to another, till all the payments are absorbed; provided, the time between one payment and another be one year or more. But if any payment be made before one year's interest hath accrued, then compute the interest on the principal sum dye on the obligation 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 that sum from the principal and interest added as above. If any payment be made of a less sum than the interest arisen at the time of such payment, no interest is to be computed, but only on the principal sum, for any period.” -Kirby's Reports, page 49.

This Rule is founded on the following principles : 1. That, when obligations have run on interest for 1 or more years, interest is not due at intervals of time less than one year.

2. If an endorsement be made after one year's interest has accrued, but which is less than the interest at the time of such endorsement, then the endorsement shall not bear interest like endorsements made before a year's interest has become due.

3. “Interest is allowed on all endorsements from the time of their payment, until the year has elapsed, or until an endorsement is made beyond the year, which with the preceding endorsement or endorsements, and its or their interest, equals or exceeds the interest due at the time of such endorsement." Note. --Legal interest in the New England states is 6 per cent.

1. Suppose a note was given on demand for 1000 dollars, dated February 1št, 1825; on which were the following en dorsements : 1. April 1, 1826, Received,

$80. 2. August 1, 1826,

30. 3. October 1, 1827,

10.

4. December 1, 1827,

600. 5. May 1, 1828.

200. What was the balance due on the note, October 1, 1828, at 6 per cent?

Ans. $263,93cts. $1000 Principal.

70 Int. to the 1st end't., being 1 year and 2 months. 1070 Amount.

80 1st Endorsement. 990 Principal remaining due April 1, 1826.

99 Int. to the 4th end't., being 1 year and 8 months.
1089 Amount to the 4th endorsement.
30 2d Endorsement.

2,40 Interest to the 4th endorsement:
32,40
10, 3d Endorsement, which does not bear interest, be-

cause, 1 year's int. has accrued on new principal. 600, 4th Endorsement,

Tort from 1089 dollars. 642,40 veuns 446,60 Principal remaining due, Dec. 1, 1827. 22,33 Int. to.Qet. 1, 1828, being 10 months. 468,93 Amount to October 1, 1828. 200, 5th Endorsement. 5,

Interest to Oct. 1, 1828, being 5 months. 205, Amount-deduct from $468,93 cents. $ 263,93 cents. Balance due October 1, 1828.

2. Suppose a bond or note, dated May 10, 1824, was given for 2000 dollars, interest at 6 per cent, upon which were the following endorsements, viz. : 1. March 10, 1825, Received,

$800. 2. May 10, 1826,

400. 3. September 10, 1827,

300. What remained due January 10, 1829 ?

Ans. $821,73 cents 7 mills.

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The following Rule was established by the Superiour Court of the state of Massachusetts in 1821.

RULE III.-"Compute the interest on the principal sum, from the time when the interest commenced, to the first time when a 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 interest, as upon the first principal, and from the amount subtract the payment; and proceed in this manner, to the time of the judgment or settlement."Mass. Reports, Vol. 17, page 418.

This Rule involves the same principles as the Rule FIRST established for the practice of the Courts in the State of New York.

1. That interest is due at any time when a payment is made; and that the payment first goes to discharge the interest, and then to reduce the principal; but interest is never allowed to form a part of the principal, so as to carry interest; for the effect in such case would be to give Compound Interest, which the law does not allow.

2. Where the interest exceeds the payment, interest is continued on the same principal, till the amount of the payments exceed the interest.

EXAMPLES. 1. Suppose a note was given on demand for $1000, dated Feb. 1, 1825, on which were the following endorsements. 1. April 1, 1826, Received.

$ 80. 26 August 1, 1826,

30. 3. October 1, 1827,

10. 4. December 1, 1827,

600. 5. May 1, 1828,

200. What remained due on the note, October 1, 1828, at 6 per cent?

Ans. $265,87cts. 2m. $ 1000 Principal.

70 Interest to the 1st end't., being 1 year 2mo. 1070 Amount to the first endorsement.

80 Ist Endorsement. .990 Principal remaining due, April 1, 1826.

19,80 Int. to the 2d endorsement, being 4mo. 1009,80 Amount to 2d endorsement.

30, 2d Payment. 979 80 Principal remaining due August 1, 1826.

Carried over.

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Brought over. 979,80 Principal remaining due August 1, 1826. 68,58,6 Interest to the 3d endorsement. 9,79,8 Int. to the 4th endorsement on the same princi

pal; the interest exceeding the payment,
1058,18,4 Amount to the 4th endorsement.
10

3d Endorsement.
600 4th Endorsement.
610 Sum of the 3d and 4th end'ts: deducted.
448,18,4 Principal remaining due Dec. 1, 1827.

11,20,4 Interest to the 5th payment:
459,38,8 Amount to the 5th payment.
200, 5th Endorsement.
259,38,8 Principal remaining due May 1, 1828.

6,48,4 Interest to October 1, 1828. $265,87,2 Balance due on note, October 1, 1828. 263,93 Balance due according to Rule II.

1,94,2 Difference in the two methods of work. 2. Suppose a bond or note was given for 1200 dollars, at 6 per cent interest, dated October 15th, 1826, on which were the following payments, viz. : Oct. 15th, 1827, Received $1000; April 15th, 1828, Rec'd $ 200. What 'remained due October 15th, 1828?

Ans. $82,56cts. 4m. Some of the States have adopted the following Rule: lst. Find the amount of the principal and interest for the whole time; then find the amount of each endorsement, from the time was made to the time of settlement; then from the first amount deduct the sum of the ans unts of the several endorsements, and the remainder will be the balance due.

This Rule is founded on the following principle : That interest is not due until the obligation is paid, and consequently interest must be allowed on endorsements from the time they were severally made, until the time of settlement.

As this Rule involves an absurdity, we therefore do not think it necessary to advert to it further than to show its fallacy. Suppose a man gives his note on demand for $ 100, and it runs for 22 years, he, at the end of each year, paying 7 dollars, which is the lawful'interest computed at 7 per cent, and justly due to the lender at the end of each year for the use of his money, brings the 'lender in his debt six dollars and nineteen cents, without paying him one cent of the principal; because 100 dollars, in 22 years, amounts to 254 dollars; and the 7 dollars endorsed at the end of the first year running on interest according to this rule, 21 years amounts to 17 dollars and 29 cents; and the endorsement, Ý dollars,' made at the end of the second year, amounts to 16 dollars and 80-cents, and so on, casting the interest on the $7 paid at the end of each year to the time of settlement, or to the twenty-second year from the date of the note, and adding the several amounts, we find the total amount to be 260 dollars 19 cents, which is $6,19 cents more than the amount of the note, so that it is evident, according to this method of computing interest, that the borruwer would get the lender in debt in 22 years, by barely paying him, at the end of each year, the interest justly due on the note ; the rule is therefore absurd.

NOTE.—The difference of opinion relative to the computation of lawful interest, arises from the principle assumed in respect to the time when interest bécomés duë.

There is another method of casting Interest, which frequently shortens the work, especially where the rate is six

per cent.

RULE.-Take half the greatest even number of months for a multiplier; and if there be an odd month, reckon it 30 days, and to the 30 add the given days, if any; then divide the days by 6, placing the quotient at the right of half the greatest even number of months, for å decimal, and take the whole for a multiplier, by which multiply the principal; pointing off from the product two figures further to the left hand than the usual place for decimals, and the product will be the interest, for the given time, at 6 per cent.

Should there be å remainder after taking one sixth of the days, reduce it to a vulgar fraction, that is, to its proper part or parts of 6 days, for which take aliquot parts of the multiplicand, thus:

If the remainder be 1=, divide the multiplicand by 6
If
2=},

3
If
3=1,

2 If 4=ž,

by 3 twice If

5=, and , -- by 2 and 3. The quotients arising must be added to the product of the

principal, multiplied by half the months, &c.' The product will then be the interest required.

Or, instead of taking aliquot parts of the principal, for the remaining days, you may continue the division when dividing the days by 6, to two decimal places, which will give you a multiplier sufficiently accurate in business.

Should the rate be any other than 6 per cent, first find the interest at 6 per cent, then divide the interest, already found, by such parts as the interest at the rate required, exceeds or falls short of the interest at 6 per cent, and the quotient added or subtracted from the interest at 6: per cent, as the case may require, will give the interest.

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