555. ILLUSTRATIVE EXAMPLE. A note for $ 600, dated June 20, 1874, had payments indorsed upon it as follows: Oct. 2, 1874, $110.20. May 23, 1876, $ 125.25. Dec. 11, 1876, 113.20. Find the balance due Jan. 21, 1877; interest 6%. WRITTEN WORK. Principal from June 20, 1874 $ 600.00 Interest to Oct. 2, 1874 (3 mo. 12 d.). 10.20 Ainount 610.20 First payment, Oct. 2, 1874 110.20 New principal from Oct. 2, 1874 500.00 $ 42.25. 49.25 549.25 Second and third payments, $ 24 +$ 125.25 149.25 New principal from May 23, 1876 400.00 Interest to Dec. 11, 1876 (6 mo. 18 d.). 13.20 Amount 413.20 Fourth payment 113.20 New principal from Dec. 11, 1876 300.00 Interest to Jan. 21, 1877 (1 mo. 10 d.) . 2.00 Balance due Jan. 21, 1877 (Ans.) $302.00 556. The above is in accordance with The United States Rule for Partial Payments. 1. Find the amount of the principal to the time when the payment or the sum of the payments equals or exceeds the interest; take from this amount a sum equal to the payment or payments. 2. With the remainder as a new principal, proceed as before, to the time of settlement. 557. Examples for the Slate. 50. Oct. 12, 1873, I gave my note on demand, with interest at 6%, for $480; Feb. 6, 1874, I paid $ 120. What remained due Aug. 24, 1874 ? 51. I held a note for $ 500, which bore interest at 6% from May 10, 1869; Sept. 16, 1870, I received $140; July 28, 1872, I received $50. What remained due Sept. 4, 1872 ? 52. June 15, 1873, George Rich borrowed of John Jones $ 2000, and gave his note for the same, with interest at 8%. Aug. 27, 1874, a payment of $ 1450 was made, and a new note given for the balance. For what sum was the new note given ? Write the new note in proper form, dating it at Boston. 53. A note for $ 1000, dated Oct. 5, 1874, was indorsed as follows: Dec. 8, 1874, $125; May 12, 1875, $316; Sept. 2. 1875, $417. What balance was due March 9, 1876; interest 6% ? 54. What balance will be due July 1, 1881, on a note of $935 on interest from Sept. 1, 1875, and indorsed $125.75, Jan. 15, 1876; $ 250, March 25, 1877; $300, May 10, 1877; interest being 6%. (55.) $ 425. NEW YORK, July 13, 1869. Six months after date I promise to pay A. Hyde & Co. Four Hundred Twenty-five Dollars, with interest at 6%; value received. STEWART E. FRENCH. Indorsements : Aug. 9, 1871, $ 50; Nov. 17, 1872, $ 150. What was due July 12, 1873? (56.) $ 800. ST. LOUIS, July 15, 1870. For value received, We jointly and severally promise to pay H. Hooker, or order, Eight Hundred Dollars on demand, with interest at 7%. JAMES HOLLAND. HENRY HOLLAND. Indorsements: April 18, 1871, $ 100; Dec. 31, 1872, $ 70 ; June 14, 1874, $ 62.50. What was due July 14, 1875 ? F 800 558. ILLUSTRATIVE EXAMPLE. Philadelphia, July 7, 1876. Three months after date S promise to pay Moses Pinnock, or order, Eight Hundred Dollars, with interest at 6%; value received. Stephen Ruggles . Indorsements : Aug. 16, 1876, $ 200 ; Oct. 8, 1876, $ 480 ; Feb. 20, 1877, $ 49.92. What balance was due July 1, 1877 ? 559. When partial payments are made upon notes on interest for short periods of time, as upon the above, interest is often computed by the following, called The Merchants' Rule. 1. Compute interest on the principal from the time it begins to draw interest to the time of settlement, and also on each payment from the time it is made WRITTEN WORK OF EXAMPLE ABOVE. to the time of settlePrincipal on interest from July 7, '76 $800.00 ment. Interest to July 1, '77 (11 mo. 24 d.) . 47.20 Amount of note 847.20 2. Take the differPayment, Aug. 16, '76 200.00 ence between the sum Interest to July 1, '77 (10 mo. 15d.) 10.50 of the principal and Payment, Oct. 8, '76 480.00 its interest and the Interest to July 1, '77 (8 mo. 23 d.) 21.04 sum of the payments Payment, Feb. 20, '77 49.92 and their interests; Interest to July 1, '77 (4 mo. 11 d.) 1.09 this difference will 762.55 be the balance due. Balance due Ans. $ 84.65 . 560. Examples for the Slate. (57.) $1000014 WASHINGTON, Oct. 3, 1875. In two months from date I promise to pay to the order of Cyrus Parsons, at Suffolk Bank, Boston, Ten Thousand 10% Dollars, with interest at 6%; value received. IRA NORTON. Indorsements : Nov. 5, 1875, $ 672.41; Nov. 15, 1875, $7682.42 ; Nov. 16, 1875, $ 437.98; Nov. 19, 1875, $ 833.42. What was the balance due on the above when it became due ? (58.) $ 1200. BALTIMORE, April 1, 1875. One year from date, for value received, I promise to pay B. F. Bryant, or order, Twelve Hundred Dollars, with interest at 7%. ISAAC C. FELLOWS. Indorsements : April 12, 1875, $161.08; July 19, 1875, $ 224.14; July 28, 1875, $17.90; Jan. 29, 1876, $ 100.25. What was due on the above note April 1, 1876 ? For annual interest, also for Vermont, New Hampshire, and Connecticut rules for partial payments, with annual interest, see Appendix, pages 309 and 310. PROBLEMS IN INTEREST. To find the Time, baving the Interest, Principal, and Rate given. 561. ILLUSTRATIVE EXAMPLE. In what time will $ 480 on interest at 5% yield $ 36 of interest ? WRITTEN WORK. Explanation. The interest of $ 480 for 1 $ 480 x 0.05 = $ 24. year at 5% is $ 24. $36 - $ 24 = 11. Since $ 480 at 5% yields $24 of interest in 1} yr. = 1 yr. 6 mo. 1 year, to yield $ 36 it will require as many years as there are times $24 in $36, which is 13. Ans. 1 yr. 6 mo. 562. From the above may be derived the following Rule. To find the time, having the principal, interest, and rate given: Divide the given interest by the interest of the principal at the given rate for 1 year; the quotient will be the ouwmber of years. This rule may be expressed by the formula: Interest 1. Number of years Principal ~ Rate NOTE. It will often be found more convenient to divide by the interesi for 1 month or 1 day, in which case the answer will be in months or in days. 563. Examples for the Slate. In what time will (59.) $ 400 gain $20 at 6%? (62.) $ 3000 gain $ 205 at 5%? (60.) $ 500 gain $60 at 4%? (63.) $ 408 gain $ 170 at 71%? (61.) $640 gain $67.20 at 7%? (64.) $450 gain $192.30 at 8%? 65. In what time will $ 280 amount to $ 301 at 5%? NOTE. To find interest, subtract $280 from $ 301. 66. How long must a note of $ 7500 run to amount to $ 7800 at 8%? 67. In what time will $500 double itself at 1%? at 2%? at 3%? at 6%? at 10%? WRITTEN WORK. Ans. 8%. To find the Rate, having the Interest, Principal, and Time given. 564. ILLUSTRATIVE EXAMPLE. The interest on $ 200 for 10 mo. 24 d. was $ 14.40; what was the rate % ? Explanation. — The interest of $ 200 for $ 200 x 0.009 = $ 1.80. 10 mo. 24 d. at 1% is $ 1.80. $ 14.40 = $ 1.80 = 8. Since the interest at 1% on $ 200 for 10 mo. 24 d. is $ 1.80, to yield $ 14.40 the rate must be as many times 1% as there are times $ 1.80 in $14.40, which is 8. Ans. 8%. 565. From the above may be derived the following Rule. To find the rate, having the interest, principal, and time given: Divide the given interest by the interest of the principal for the given time at 1%; the quotient will be the number of the per cent. The above rule may be expressed by the formula: Interest 2. Rate = Principal Number of years 566. Examples for the Slate. 68. At what rate % will $ 360 gain $ 40.80 in 1 y. 5 mo.? 69. At what rate % will $ 100 gain $33 in 12 y. 6 mo.? |