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RULE 2. By'a statute of Massachusetts, the following rule is established to cast interest upon securities, where endorsements have been made, viz. find the interest upon the note to the time of the first payment, and add it to the priccipal ; 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 Thorndike, 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
$1000 in 1 yr. amounts to $1060 amţ. of note.
Ans. $545 due.
endorsement subtracted 500.00
a new principal $530.00 $530.00 cts: in 6 mo. more amts. to $345.90 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
that he paid $5000 of it in 3 months which was en-
Amount of $20000.00 in one year $21200·00
due on settlement. Ans. 815975.00
endorsements subtracted 5000.00
new principal $15300.00
Amount of new principal in 9 mo.
Note I. The reader will observe that the two methods do not agree, and the reason is obvious : in the first example by sule 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 inet Mr Thorndike's deinand, viz. 515,) and Mr.
Thorndike would have demanded of him 1000 dollars, and one year's interest; viz. 81060-515–8545 due on settlement, saine 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 inonths ; 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.
830 X:06x 6 months=-90 cents the difference as before.
Note Ill.-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, aud bore interest the remaining nine months.
of n d
$300 X.06X9 months $13.50.
These notes will be abundantly sufficient to explain the cause of the difference in the two methods of operation ; and I submit it to the publick to judge of the correctness of the two methods allud
For my own part I cannot conceive any proprie'y in adding the interest to the principal, till one year has expired; and I do not see any injustice in ihe creditor's paying interest for the money received within the year, if the debtor pays him interest for all the money received of him, to the end of the year, therefore I give my preference to the first method of operation.
SHEWING THE AMOUNT OF ONE DOLLAR FOR ANY NUM
BER OF YEARS UNDER THIRTY THREE; ALSO THE
AMOUNT OF ONE DOLLAR FOR ANY NUMBER OF
MONTHS UNDER TWELVE.
1993. umt. YI'S.
1.66 | 22 2.32 33 2.98 | 11 1.0551
Note - This table is a very easy method of casting interest, and would be very useful in a counting room; the amount of one dollar being known for any number of years, or months, the amount of any other number may be found hy multiplying the numbers together.
t f t
1. What will 16 dollars amount to in six years
2. What will 211 dollars amount to in 9 years at
6. What will 1 dol. amount to in 8 years, 6 mo. at 6 per cent. ?
COMPOUND INTEREST. DEFINITION.-Compound interest is the interest of the interest; when interest is not paid yearly it ought to become a part of the principal.
RULE. Find the interest of the principal for one year, and to the interest add the principal, this sum will be the principal for the second year; thus continue to add the last interest and last principal together, until you have found the amount for the number of years required ; from the last amount subtract the first principal, and the remainder is the
100 1st principale
METHOD SECOND. Rule. Find what aliquot part the rate per cent. is of 100; divide the principal by the aliquot part, or parts, and set the quotient, or quotients under the principal, the same as quotients in short division ;* add the quotients and principal together, the sum is the second principal; divide the second principal in the same manner, by the aliquot parts, &c. the sum of the quotients, &c. is the second principal; thus cèntinue till you have found the amount required; from which subiract the first principal, the remainder is the interest sought.
* If the rate per cent. is no aliquot part of an hundred, use two, or more numbers that will make the rate per cent. and are aliquot parts of an hundred ; divide by these numbers, add the quotients, the sum will be the answer.