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 judgement 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. What remained due on the note, October 1, 1828, at 6 per cent? $1000 Principal. Ans. $265,87cts. 2m. 70 Interest to the 1st. end't., being 1 year 2mo. 1070 Amount to the first endorsement. 80 1st. Endorsement. 990 Principal remaing due, April 1, 1826. 1009,80 Amount to 2nd. endorsement. 30, 2nd. Payment. 979,80 Principal remaining due August 1, 1826. Brought over 979,80 Principal remaining due August 1, 1826. 9,79,8 In. to the 4th endorsement on the same prinči- 1058,18,4 Amount to the 4th endorsement. 10 600 610 3d. Endorsement. 4th. Endorsement. Sum of the 3d. and 4th end'ts. deducted. 448,18,4 Principal remaining due Dec. 1, 1827. 459,38,8 Amount to the fifth payment. 200, 259,38,8 Principal remaining due May 1, 1828. $265,87,2 Balance due on note, October 1, 1828. 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. 15, 1827, Rec'd. $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: 1st. Find the amount of the principal and interest for the whole time; then find the amount of each endorsement, from the time it was made to the time of settlement; then from the first amount deduct the sum of the amounts 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 consequent ly 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 aç cording to this rule, 21 years amounts to 17 dollars, and 29 cents; and the endorsement, 7 dollars, made at the end of the second year, a mounts to sixteen 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 borrower 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 becomes due. 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 a 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 a 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 1-1, divide the multiplicand by 6 The quotients arising must be added to the product of the principal, multiplied by half the months, &c. The product wil 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 ac curate in business. Should the rate be any other than 6 per cent, first find the interest at 6 per cent, then divid 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. EXAMPLES. 1. What is the interest of 500 dollars for 1 year 3m. and 15 days, at 6 and 7 per cent? 38,75cts. Om. interest at 6 per cent. Ans. 45,20cts. 8m. interest at 7 per cent. DEM.-It is plain, when we multiply by half the even number of months, we do the same as multiplying by the per cent, that is, 6 per cent; for suppose the number of months, were 12, then half the number would be six, the same as the per cent, that is, 6 per cent, and suppose we call the odd month 30 days, and divide by 6, the quotient would stand as 5 tenths of 2 months; hence the reason of the rule is manifest. NOTE I-If the interest of 500 dollars, in the preceding example, had been required at 5 per cent, then the $6,45cts. and 8 mills, should have been deducted from $38,75 cents; the remainder would have been the interest at 5 per cent. NOTE II-Where there are days, of a number less than 6, so that 6 cannot be contained in them, put a cipher in the place of the decimal at the right hand of the months in the multiplier, so that the quotients, when the multiplicand is divided for the days, may stand in their proper place. 2. What is the interest of $300,50 cents for 2 years, 5 months and 9 days, at 7 per cent? Ans. $51,36cts. [Commission and SIMPLE INTEREST. Factorage.] 159 COMMISSION, OR FACTORAGE, Is an allowance of a certain per cent, to a Factor or Person engaged in buying and selling goods for his employer. A Factor is an agent employed to transact business for another. The work is precisely the same as casting the interest on the same sum for one year; but the Factor can only receive for his services from his employer, the per cent on the sales or purchases which he has made; thus, if the Factor buys or sells goods to the amount of one hundred dollars, at three per cent, he receives only three dollars for his services, and the remaining part of the gain, if any, goes to his employer. $1000 EXAMPLES. 1. What may a factor demand from his employer, when he sells goods to the amount of $1000, and is allowed 3 per cent, for his services? Ans. $35. The learner will perceive, that the operation of the work here, is exactly the same as computing interest on one thousand dollars for one year, at 3 per cent, and 35 dollars is what the factor receives for his services for selling the goods for the benefit of his employer. 31 3000 Ans. $35,00 2. What will the commission of 500 dollars come to, at 5 per cent? Ans. $27,50cts. NOTE.-Commission here means the premium arising from the per cent on the given sum, which is the reward for the agent's services. 3. Required the commission of fifteen hundred dollars, at 3 per cent? Ans. $45. 4. What may a factor demand for laying out $1200, commission at 21 per cent? Ans. $30. BROKERAGE, Is an allowane of a certain per cent, to persons assisting merchants or factors, in their purchases and sales. The work is performed the same as in Simple Interest, where Interest is to be computed for one year; and the Broker receives his per cent for his services; thus, if he assists his employer in buying or selling goods to the amount of one hundred dollars at 3 per cent, he receives three dollars and fifty cents for his services. EXAMPLES. 1. What is the brokerage upon 1500 dollars, at 1 per cent? Ans. $22,50cts: |