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Indorsements: June 16, 1859, two hundred dollars; August 1, 1860, ono hundred and sixty dollars; November 16, 1860, seventy-five dollars; February 1, 1862, two hundred and twenty dollars. What was due August 1, 1862 ?

Ans. $ 417.822.

OPERATION

Principal,

$ 900.00

56.25 Interest from June 1, 1858, to June 16, 1859, 124 months,

956.25 First payment,

200.00

756.25 Interest from June 16, 1859, to August 1, 1860, 134 months, 51.046

807.296 Second payment,

160.000

647.296 Interest for 1 year,

38.837

686.133 Am't of 3d pay't, from Nov 16, 1860, to Aug. 1, 1861, 84mo., 78.187

607.946 Interest from Aug. 1, 1861, to Aug. 1, 1862, 12 months, 36.476

644.422 Am't of 4th pay't, from Feb. 1, 1862, to Aug. 1, 1862, 6mo., 226.600 Balance due August 1, 1862,

$ 417.822

MERCHANTS' RULE.

372. 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.

EXAMPLES (1.) $ 1728.

Baltimore, January 1, 1853. For value received, I promise to pay Riggs, Peabody, & Co., or order, on demand, one thousand seven hundred and twentyeight dollars, with interest.

John PAYWELL, JR. Indorsements: March 1, 1853, three hundred dollars; May 16, 1853, one hundred and fifty dollars; September 1, 1853, two hundred and seventy 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,

RICHARD FLETCHER. Payments: March 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.

WILLIAM AMSDEN. Indorsement: July 1, 1857, two hundred dollars.

What was due April 1, 1858, the rate of interest being 7 per cent. ?

Ans. $ 324.50.

ANNUAL INTEREST.

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 due 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 ?

OPERATION.

Interest on $ 500 for 4 years 6 months,

135.00 Interest on $30 for 3 years 6 months,

= interest
2
years 6 months, on $ 30 for

14.40
1 year
6 months,

8

years, 6 months, Annual interest, $ 149.40 Principal,

500.00 Amount due, $ 649.40 30 0.00

30 66 30 66 306

66

COMPOUND INTEREST.

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 ?

FIRST OPERATION.

Principal for 1st year,

$ 3 0 0 Interest of $ 1 for 1 year,

.0 6 We first multiply the

given principal by the Interest for 1st year,

18.00

number denoting the

3 0 0.0 0 interest of $1 for one Principal for 2d year, 3 18.00

year, and add the in

terest thus found to .06

the principal for the Interest for 2d year,

1 9.0 800 amount; on which as a 31 8.00

new principal we find

the interest for the secPrincipal for 3d year, 3 3 7.08 ond year, and proceed as

.06 before; and so also with

the third year. From Interest for 3d year,

2 0.2 2 48 the amount of the last 3 3708

year we subtract the

first principal, and obAmount for 3 years,

3 5 7.3 0 48

tain the compound inFirst principal,

terest for 3 years. Comp. int. for 3 years, $ 5 7.30 48, Ans.

SECOND OPERATIOX

Principal for 1st year,

$ 3 0 0.0 0 to of the principal,

1 5.0 0 of the interest at 5 per cent.,

3.0 0 Principal for 20 year,

318.0 0 Amount for 1st year at o of the principal,

15.90

[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 my of the principal,

1 6.8 4 5

[6 per cent. of the interest at 5 per cent.,

3.3 70

3 5 7.3 04 Amount for 3d year First principal,

30 0.00

[at 6 per cent. Compound interest for 4 years, $ 57.3 04 Ans.

In the second operation the work is somewhat abridged, by finding the interest for each year at 6 per cent. by taking zo 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 time 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 find the amount of the given principal, and from it to subtract the sum of the several amounts of the indorsements.

EXAMPLES.

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. 377. The computation of compound interest is rendered more expeditious by means of the following

TABLE,

OWING THE AMOUNT OF ONE DOLLAR AT COMPOUND INTEREST FOR ANY

NUMBER OF YEARS NOT EXCEEDING FIFTY.

5 per cent.

No. 3 per cent. 34 per cent.

1 1.030 000 1.035 000 2 1.060 900 1.071 225 3 1.092 727 1.108 718 4 1.125 509 1.147 523 5 1.159 274 1.187 686 6 1.194 052 1.229 255 7 1.229 874 1.272 279 8 1.266 770 1.316 809 9 1.304 773 1.362 897 10 1.343 916 1.410 599 11 1.384 234 1.459 970 12 1.425 761 1.511 069 13 1.468 534 1.563 956 14 1.512 590 1.618 694 15 1.557 967 1.675 349 16 1.604 706 1.733 986 17 1.652 848 1:794 675 18 1.702 433 1.857 489 19 1.753 506 1.922 501 20 1.806 111 1.989 789 21 1.860 295 2.059 431 22 1.916 103 2.131 512 23

1.973 587 2.206 114 24 2.032 794 2.283 328 25 2.093 778 2.363 245 26 2.156 591 2.445 959 27 2.221 289 2.531 567 28 2.287 928 2.620 177 29 2.356 566 2.711 878 30 2.427 262 2.806 794 31 2.500 080 2.905 031 32 2.575 083 3.006 708 33 2.652 335 3.111 942 34 2.731 905 3.220 860 35 2.813 862 3.333 590 36 2.890 278 3.450 266 37 2.985 227 3.571 025 38 3.074 783 3.696 011 39 3.167 027 3.825 372 40 3.262 038 3.959 260 41 3.359 899 4.097 834 42 3.460 696 4.241 258 43 3.564 517 4.389 702 44 3.671 452 4.543 342 45 3.781 596 4.702 358 46 3.895 044 4.866 941 47 4.011 895 5.037 284 48 4.132 252 5.213 589 49 4.256 219 5.396 065 50 4.383 906 5.584 927

4 per cent.

6 per cent. 7 per cent. 1.040 000 1.050 000 1.060 000 1.070 000 1.081 600 1.102 500 1.123 600 1.144 900 1.124 864 1.157 625 1.191 016 1.225 043 1.169 859 1.215 506 1.262 477 1.310 796 1.216 653 1.276 282 1.338 226 1.402 552 1.265 319 1.340 096 1.418 519 1.500 730 1.315 932 1.407 100 1.503 630 1.605 781 1.368 569 1.477 455 1.593 848 1.718 186 1.423 312 1.551 328 1.689 479 1.838 459 1.480 244 1.628 895 1.790 848 1.967 151 1.539 454 1.710 339 1.898 299 2.104 852 1.601 032 1.795 856 2.012 196 2.252 192 1.665 074 1.885 649 2.132 928 2.409 845 1.731 676 1.979 932 2.260 904 2.578 534 1.800 944 2.078 928 2.396 558 2.759 032 1.872 981 2.182 875 2.540 352 2.952 164 1.947 901 2.292 018 2.692 773 3.158 815 2.025 817 2.406 619 2.854 339 3.379 932 2.106 849 2.526 950 3.025 600 3.616 526 2.191 123 2.653 298 3.207 135 3.869 684 2.278 768 2.7 85 963 3.399 564 4.140 562 2.369 919 2.925 261 3.603 537 4.430 402 2.464 716 3.071 524 3.819 750 4.740 530 2.563 304 3.225 100 4.048 935 5.072 367 2.665 836 3.386 355 4.291 871 5.427 433 2.772 470 3.555 673 4.549 383 5.807 353 2.883 369 3.733 456 4.822 346 6.213 868 2.998 703 3.920 129 5.111 687 6.648 838 3.118 651 4.116 136 5.418 388 7.114 257 3.243 398 4.321 942

5.743 491 7.612 255 3.373 133 4.538 039 6.088 101 8.145 113 3.508 059 4.764 941 6.453 387 8.715 271 3.648 381 5.003 189 6.840 590 9.325 340 3.794 316 5.253 348 7.251 025 9.978 114 3.946 089 5.516 015 7.686 087 10.676 581 4.103 933 5.791 816 8.147 252 11.423 942 4.268 090 6.081 407 8.636 087 12.223 618 4.438 813 6.385 477 9.154 252 13.079 271 4.616 366 6.704 751 9.703 507 13.994 820 4.801 021 7.039 989 10.285 718 14.974 458 4.993 061 7.391 988 10.902 861 16.022 670 5.192 784 7.761 588 11.557 033 17.144 257 5.400 495 8.149 667 12.250 455 18.344 355 5.616 515 8.557 150 12.985 482 19.628 460 5.841 176 8.985 008 13.764 611 21.002 452 6.074 823 9.434 258 14.590 487 22.472 623 6.317 816 9.905 971 15.465 917 24.045 707 6.570 528 10.401 270 16.393 872 25.728 907 6.833. 349 10.921 333 17.377 504 27.529 930 7.106 683 11.467 400 18.420 154 29.457 025

NOTE. — If each of the numbers in the table be diminished by 1, the remainder will denote the interest of $1, instead of its amount.

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