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ART. 829.-Rule for finding Compound Interest. Find the amount of the principal for the first period on which interest is due, and make it the principal for the second period.
Find the amount of the new principal for the second period, and make it the principal. for the third period. Continue in this manner through each period and fraction of a period to the end of the given time.
The given principal subtracted from the last amount, is the compound interest required.
Find the compound interest on-
4. $125 for 2 years 9 months at 4% interest, compounded semi-annually.
5. Find the amount of $1,000 for 4 years at 4% compound interest.
6. Find the amount of $75.75 for 3 years 3 months 24 days at 5% compound interest.
7. Find the amount of $1,848 for 5 years 4 months 15 days at 7% compound interest.
8. What is the amount of $1,200 for 2 years at 8%, interest compounded semi-annually ?
9. What is the difference between the simple and the compound interest on $180 for 2 years at 8%, if the interest is compounded quarterly ?
10. Illustrate compound interest by an original problem.
NOTE.—Elaborate tables are published from which the interest and amount of any sum of money, for any given time at any rate, are easily ascertainable. Having learned the principles and methods governing these computations the pupils can have recourse to such aid should the necessity arise.
ART. 330.-A Promissory Note is a written promise to pay on demand or at a specified date a certain sum of money.
ART. 331,—The Face of the note is the sum named in it. When a note bears interest, its amount is the Face.
ART. 332.—The Maker or Drawer of a note is the party that signs it, and thereby promises to pay it.
ART. 333.—The Payee of a note is the party to whom, or to whose order, it is payable.
ART. 334.—The Holder of a note is its legal owner.
ART. 335. —The Indorser of a note is the party who writes his name on its back, and thereby becomes surety for its payment. Should the drawer of a note fail to pay it when due, the indorser is liable.
ART. 336.—A Joint Note is one signed by two or more persons, who are jointly liable for its payment.
ART. 337.-A Joint and Several Note is a note signed by two or more parties, who are jointly and singly liable for its payment.
ART. 338.—A Demand Note is one payable on demand.
ART. 339.—A Time Note is a note payable at a future specified time.
ART. 340.—A Negotiable Note is a note made paye able to bearer, or to the order of the payee.
ART. 341.—In some of the States Three Days of Grace are allowed on all time notes after the time for payment expires.
A joint note reads: “We jointly promise to pay,” etc., while a joint and several note reads: “We jointly and severally promise to pay,” etc. Demand notes are payable on presentation without grace, and bear legal interest after a demand has been made. An indorser on a demand note is responsible only for a limited time, variable in different States. Notes falling due on Sunday or on a holiday must be paid the day previous. Notes made on Sunday are void. All notes should contain the words “ value received."
ART. 342.-Partial Payments are payments in part of notes or written obligations bearing interest.
ART. 343.—An Indorsement is a statement of the part payment made and the date of making it. It is written across the back of the note.
The rule prescribed by the Supreme Court of the United States for partial payments, and adopted by many of the States, is based on the following principles :
ART. 344.- Payments must first be applied to the discharge of interest then due, and the remainder, if any, to the payment of the principal.
Unpaid interest must not be added to the principal : only unpaid principal can draw interest.
ART. 345.-United States Rule.—Find the amount of the principal to the time of the first payment ; if the payment equals or exceeds the interest then due, subtract the payment from the amount, and the remainder forms a new principal.
If the payment is less than the interest, find the amount of the first principal to the time when the sum of the payments equals or exceeds the interest due, and subtract
the sum of the payments from the amount of the principal, using the remainder for a new principal.
Proceed in this manner with the remaining payments until the date of settlement.
WRITTEN EXERCISES. 1. $800.
Austin, Texas, October 1, 1884. On demand I promise to pay A. S. Manson, or order, Eight Hundred Dollars, with interest at 8 per cent., for value received.
Oscar E. Hazen.
The following payments were indorsed on this note :
Jan. 1, 1885, $80; April 19, 1885, $10; September 1, 1885, $240 : what was due Jan. 1, 1886 ?
Process. $800 = 1st principal.
16 = Int. from Oct. 1, '84, to Jan. 1, '85 (3 mo.). $816 = lst amount.
80 = 1st payment. $736 = 2d principal.
39.25 = Int. from Jan. 1, '85, to Sept. 1, '85 (8 mo.). $775.25 = 2d amount.
250. = sum of 2d and 3d payments. $525.25 = 3d principal.
14.01 = Int. from Sept. 1, '85, to Jan. 1, ’86 (4 mo.). $539.26 = Amount due at settlement.
Analysis.-We first compute the interest on the principal to the date of the first payment.
This is $16. Hence, on that day, Oscar E. Hazen owes $816. Instead of paying the note with interest, he paid $80 on it. He then owed $816 – $80 = $736.
The interest on this new principal to the next payment is $17.66, while the payment is only $10. As directed by the Supreme Court of the United States, we merely record the payment of the $10, and use the principal unchanged until the next payment is made.
The interest on $736 to the next payment is $21.59, while the payment is $240, which is in excess of the accrued interest. We therefore add the two interests together, and find they amount to $39.25, which we add to the principal, $736, and find the total indebtedness to be $775.25. From this sum we subtract the sum of the two payments ($10 + $240), obtaining a remainder of $525.25, which is the total indebtedness of Mr. Hazen, September 1, 1885. Instead of settling his indebtedness at that time he waited until January 1, 1886. Hence, he must pay the principal, $525.25, together with the interest to January 1, 1886. This interest is $14.01, which, added to the principal, gives $539.26, the total indebtedness of Mr. Hazen, January 1, 1886.
2. A mortgage of $1,275.50, dated Cincinnati, July 1, 1883, had the following indorsements :
Received, Jan. 1, 1884, $600; Oct. 19, 1884, $250 ; Jan. 18, 1885, $300; September 18, 1885, $175. It was paid off March 1, 1886 : what sum was then due, interest being computed at 6% ?
3. A note for $675, dated Milwaukee, March 4, 1884, had indorsements as follows:
Aug. 16, $180; Nov. 30, $15; Feb. 27, 1885, $10; May 11, $240; Dec. 31, $150 : what was due April 1, 1886, at 7% interest ?
4. A note for $1,450, dated New Orleans, February 3, 1884, was indorsed as follows :
April 3, 1884, $64.10; July 9, 1884, $168.67; Nov. 18, 1885, $20; March 18, 1886, $21 : what was due June 14, 1886, interest at 5% ?