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Payments: July 11,1858, twelve dollars and twenty-five cents; August 15, 1854, two dollars and ten cents; July 9, 1855, three dollars and twelve cents; August 21, 1855, thirty-seven dollars and eighteen cents.
What was due December 17, 1855? Ans. $ 10.222.
(5 ) $ 1000. New Fork, January 1, 1850.
For value received, I promise to pay James Johnson, or order, on demand, one thousand dollars, with interest at seven per cent.
Samuel T. Fortune.
Indorsements: September 28, 1850, one hundred and forty-four dollars; March 1, 1851, twenty dollars; July 17, 1851, three hundred and sixty dollars; August 9, 1851, one hundred and ninety dollars; September 25, 1852, one hundred and seventy dollars; December 11, 1853, two hundred dollars; July 4, 1855, seventy-five dollars.
What was due June 1, 1857? Ans. $7.61.
371 i The Supreme Court of the State of Connecticut has adopted the following
Rule. — 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. If 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 lime between one payment and another be one year or more.
If any payments be made before one year's interest has accrued, then compute the interest on the principal sum due on the obligation for One Year, add it to the principal, and compute the interest on the sum vaid from the time it teas 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 payments 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.
Note. — If a year extends beyond the time of settlement, find the amount of the remaining principal to the time of settlement; find also the amount of the indorsement or indorsements, if any, from the time they were paid to the. time of settlement, and subtract their sum from the amount of the principal.
(1.) $ 900. New Haven, June 1, 1858.
For value received, I promise to pay J. Downs, or order, nine hundred dollars, on demand, with interest.
James L. Emerson.
/ndorsements: June 16, 1859, two hundred dollars; August 1, 1860, one hundred and sixty dollarsj November 16, 1860, seventy-five dollars; rebruary 1, 1802, two hundred and twenty dollars.
What was due August 1, 1862? Ans. $ 417.822.
Interest from June 1, 1858, to June 16, 1859, 12i months, 56.25
First payment, 200.00
Interest from June 16, 1859, to August 1, 1860, 13^ months, 51.046
Second payment, 160.000
Interest for 1 year, 38.837
Am't of 3d pay't, from Nov 16, 1860, to Aug. 1,1861,8£mo., 78.187
Interest from Aug. 1, 1861, to Aug. 1, 1862, 12 months, 36.476
Am't of 4th pay't, from Feb. 1, 1862, to Aug. 1, 1862, 6mo., 226.600 Balance due August 1, 1862, .... $417.822
"* 373. It is customary with merchants, when partial payments are made of notes or other debts, when the note or debt is settled within a year after becoming due, to adopt the following
Rule. — Find the amount of the principal for the whole time. Then find the amount of each endorsement from the time it was paid until settlement, and subtract their sum from the amount of the principal.
(1.) $1728. Baltimore, January 1, 1853.
For value received, I promise to pay Riygs, Peabody, Co., or order, on demand, one thousand seven hundred and twentyeight dollars, with interest. John Patwell, Jr.
Indorsements: March 1, 1853, three hundred dollars; May 16, 1853, one hundred and fifty dollars; September 1, 1853, two hundred and seventv dollars; December 11, 1853, one hundred and thirty-five dollars.
What was due at the time of payment, which was December 16, 1853? Ans. $948.03.
(2.) $700. Montpelier, February 4, 1854.
For value received, we jointly and severally promise to pay James Thomas, or order, on demand, seven hundred dollars, with interest. Sampson Phillips,
Payments: Mnrch 18, 1854, one hundred and sixty dollars; June 24, 1854, two hundred dollars; September 11, 1854, one hundred and twenty dollars; October 5, 1854, sixty dollars.
What was due on this note Nov. 28, 1854? Ans. $ 180.43. (3.) $ 500. Detroit, January 1, 1857.
For value received, three months after date I promise to pay to the order of James Francis five hundred dollars.
Indorsement: July 1, 1857, two hundred dollars.
What was due April 1, 1858, the rate of interest being 7 per cent.? Ans. $324.50.
373. When no payments have been made on a note, especially when written "with interest annually," the courts of some states allow interest on the annual interest, in the nature of damages for its detention, and sanction the following
Rule. — Find the interest on the principal for the whole time and the interest on each year's interest from the time it may be du* until paid. The sum of these interests will be the annual interest.
Ex. 1. L. Jones has J. Perry's note, dated January 1, 1861, for $ 500, with interest to be paid annually, at 6 per cent. What was due, on the note, July 1, 1865?
Interest on $ 500 for 4 years 6 months, ... $ 135.00 Interest on $ 30 for 3 years 6 months, ^ = interest ")
"" 30 " 2 years 6 months, I on $ 30 for > 14.40 "" 30 " 1 year 6 months, j 8 years, J "" 30" 6 months, J Annual interest, $ 149.40
Amount due, $ 649.40
374. Compound Interest is interest on the original principal with its interest added when remaining unpaid after becoming due.
When the interest is added to the principal at the end
of every year, and a new principal is thus formed yearly, it is said to compound annually; when the interest is added to the principal so as to form a new principal half-yearly, it is said to compound semiannually.
375. Compound interest is based upon the principle, that, if the borrower does not pay the interest as it becomes due at stated times, it is no more than just for him to pay interest for the use of it, so long as he shall have it in his possession.
Note. — Compound interest is not favored by the laws, though it is not usurious. A contract or promise to pay money with compound interest cannot generally be enforced, being only valid for the principal and legal interest.
376. To find the compound interest of any sum of money at any rate per cent, for any time.
Ex. 1. What is the compound interest of $ 300 for 3 years?
Comp. int. for 3 years, $ 5 7.3 0 4 8, Ans.
Principal for 1st year, $300.00 % $ of the principal, 1 5.0 0
£ of the interest at 5 per cent., 3.0 0
Principal for 2d year, 3 1 8.0 0 Amount for 1st year at
^'ij of the principal, 1 5.9 0 [6 per cent.
^ of the interest at 5 per cent., 3.1 8
Principal for 3d year, 3 3 7.0 8 Amount for 2d year at
J\j of the principal, 1 0.8 4 5 [6 per cent.
| of the interest at 5 per cent., 3.3 7 0
3 5 7.3 0 4 Amount for 3d year First principal, 3 0 0.0 0 [at 6 per cent.
Compound interest for 4 years, $ 5 7.3 0 4 Ans.
In the second operation the work is somewhat abridged, by finding the interest for each year at 6 per cent. by taking fa of the principal for the interest at 5 per cent., and \ of that for interest at 1 per cent.
Rule. —Find the interest of the given sum to the time the interest becomes due, and add it to the principal. Then, find the interest on this amount as a new principal, and add the interest to it, as before. Proceed in the same manner for each successive period when the interest becomes due until the lime of settlement.
Subtract the principal from the last amount, and the remainder will be the compound interest.
Note. — When partial payments have been made on notes at compound interest, it is customary to fiiid the amount of the given principal, and from it to subtract the sum of the several amounts of the indorsements.
2. What is the amount of $ 500 for 3 years at compound interest? Ans. $ 595.508.
3. What is the compound interest of $ 970 for 2 years 9 months and 24 days? Ans. $ 173.295.
4. What is the compound interest of $ 300 for 4 years 6 months, at 7 per cent.? Ans. $ 107.001.
5. What is the compound interest of $316 for 3 years 4 months and 18 days? Ans. $69,017.
377i The computation of compound interest is rendered more expeditious by means of the following