SIX PER CENT METHOD. 541. Oral Exercises. a. At 6%, what part of the principal is the interest for 1 year? for 2 months ? b. If the interest for 2 months is 0.01 of the principal, what part of the principal is the interest for any number of months ? Ans. One half as many hundredths of the principal as there are months. C. At 6%, what is the interest of $500 for 2 mo. ? for 4 mo.? 6 mo.? 8 mo.? 10 mo.? 5 mo. ? 7 mo. ? 15 mo.? d. If the interest for 2 months, or 60 days, is 0.01 of the principal, what part of the principal is the interest for 6 days ? e. If the interest for 6 days is 0.001 of the principal, what part of the principal is the interest for any number of days? Ans. One sixth as many thousandths of the principal as there are days. f. At 6% what is the interest of $500 for 6 days? 1 day? 2 days ? 3 days ? 12 days ? 18 days ? 24 days? 542. ILLUSTRATIVE EXAMPLE. What is the interest of $ 480 for 1 y. 3 mo. 7 d. at 6% ? at 7%? What is the amount at 7 %? Explanation. - 1 y. 3 mo. equals 0.075 15 mo. $ 480 The interest for 15 mo. at 0.0767 0.0011 6% is 0.077, or 0.075 of the princi pal. The interest for 7 days is 0.0017 2880 0.0767 of the principal. Hence the interest 3360 for ly. 3 mo. 7 d. at 6 % is 0.0764 80 of the principal. 0.076% of the prin6). $36.560 Int. at 6%. cipal is $36.56. To find the interest at 7%, we add 6.09 to the interest at 6% of itself, and $ 42.65 Int. at 7%. have for the sum $ 42.65. 480. $ 480 + $ 42.65 $ 522.65, the $ 522.65 Amt. at 7%. amount at 7% dns. $ 36.56 ; $ 42.65 ; $ 522.65. WRITTEN WORK. 543. From the foregoing may be derived the following Rule. 1. To compute interest at 6 % : Take 6 times as many hundredths as there are years, 1 half as many hundredths as there are months, and as many thousandths as there are days, and by this decimal multiply the principal. 2. To find the interest at any rate other than 6 % : Having found the interest at 6%, increase or diminish that interest by adding or subtracting such part of itself as will give the interest at the required rate. 3. To find the amount : Add the principal to the interest. NOTE I. Observe that 1%= t of 6% ; 2%= } of 6%; 3% = 1 of 6% 4%= 6% – 2 %; 5%= 6% – 1%; 7%= 6% + 1%; 73 %= 6% + (of 6%), etc. Note II. It will often be more convenient to increase or diminish the principal before taking the interest instead of increasing or diminishing the interest. Thus, in the foregoing illustrative example we might add to $480 of itself and then take 6% interest on $560. This would be the samo as the interest at 7% on $ 480, which is $ 42.65. 544. Examples for the Slate. Find the interest on $ 1 at 6% 6. For 1 y. 3 mo. 6 d. 10. For 1 y. 1 mo. 10 d. 7. For 4 y. 16 d. 11. For 1 y. 8 mo. 8. For 4 mo. 5 d. 12. For 16 y. 8 mo. 9. For 11 25 d. 13. For 7 y. 10 mo. 18 d. At 6% what is the interest 14. Of $ 300 for 2 y. 5 mo. ? 15. Of $ 36.18 for 3 y. 7 d. ? 16. Of $ 872.32 for 6 y. 2 mo. 16 d. ? 17. Of $ 130.50 for 2 y. 9 mo. 13 d. ? 18. Of $ 800.20 for 3 y. 4 mo. 12 d. ? 19. Of $ 1000 for 3 y. 10 mo. 2 d. ? 20. Of $ 25.50 for 1 y. 1 mo. 1 d. ? 21. Of $ 400.37 for 2 y. 5 mo. 26 d. ? mo. What is the interest 22. Of $ 837.36 for 3 y. 2 mo. at 7 %? 23. Of $ 187.50 for 2 mo. 12 d. at 10%? 24. Of $ 1000 from Nov. 11, 1874, to Aug. 15, 1880, at 7 %? 25. Of $ 130.16 from Feb. 7, 1874, to Dec. 1, 1878, at 8%? 26. Of $ 19.80 from Oct. 15, 1875, to April 19, 1876, at 5%? 27. Of $ 62.50 from Aug. 3, 1874, to April 11, 1875, at 71%? Find the amount 28. Of $ 540 for 3 y. 6 mo. at 6%. 29. Of $ 495.60 for 2 y. 2 mo. at 12%. 30. Of $ 830 for 5 y. 4 mo. at 8%. 31. Of $ 110.10 for 3 y. 5 mo, at 9%. 32. Of $ 896 for 2 y. 6 mo. 15 d. at 63 %. 33. Of $ 416 for 3 y. 16 d. at 7%. 34. Of $ 720 for 3 y. 9 mo. 19 d. at 8%. 35. A note for $ 150, dated July 5, 1872, was paid Mar. 17, 1874, with interest at 6%. What was the amount ? 36. I gave my note to a person, Jan. 1, 1877, for $387.20 with interest at 7 % from date. What should I pay to discharge this note Oct. 20, 1877 ? 37. Chase and Fowle bought goods to the following amounts, agreeing to pay 7 % interest from the date of purchase: July 8, 1876, $ 470; July 28, $235; Oct. 2, $206. What will be the amount due Jan. 1, 1877 ? WRITTEN WORK. Short Method for Days; Application of 6 per cent Method. 545. ILLUSTRATIVE EXAMPLE. What is the interest of $126.80 for 93 days at 6%? Explanation. — The interest at $ 126.80 6% for 60 days, or 2 months, is 0.01 of the principal. 0.01 of 1.268 Int. for 60 d. $ 126.80 may be expressed by mov0.634 66 30 d. ing the decimal point two places 0.063 3d. towards the left; this gives $1.268 Ans. $ 1.965 The interest for 1 month, or 30 66 66 66 93 d. days, is } of $1.268, or $0.634, and for 3 days it is to of $0.634, or $0.063. Adding these interests, $ 1.268 + $0.634 + $0.063 = $ 1.965. Ans. $ 1.97. 546. From the foregoing may be derived the following Rule. 1. Find the interest for 60 days at 6% by taking 0.01 of the principal. . 2. For other periods of time, Take convenient multiples or aliquot parts of the interest for 60 days. 547. Examples for the Slate. Find the interest of (38.) $ 300 for 93 d. at 6%. (40.) $ 1000 for 33 d. at 10%. (39.) * 250 for 95 d. at 7%. (41.) $ 280 for 127 d. at 12%. (42.) * 270.80 from Aug. 20 to Oct. 30 at 8%. (Exact days.] (43.) $ 416.60 from Nov. 12, 1875, to Feb. 5, 1876, at 5%. (44.) $ 1560.50 from Mar. 27, 1875, to June 7, 1875, at 9%. (45.) $ 6000 from Nov. 15, 1875, to March 7, 1876, at 6%. ACCURATE INTEREST. NOTE. The above methods of performing examples in interest being based upon the supposition that a year equals 12 months of 30 days each, or 360 days, though in common use, are not exact. The government of the United States and that of Great Britain pay accurate interest. 548. To obtain accurate interest for months and days : Find the exact number of days between the given dates, and take as many 365ths of a year's interest as there are days. 549. Examples for the Slate. 46. Find the accurate interest of $ 2000 from Mar. 1 to Aug. 10 at 5%. What is the accurate interest 47. Of $ 700 from May 7 to July 9 at 74%? 48. Of $ 20000 from April 4 to July 7 at 7%? 49. Of $ 1000 from Nov. 15, 1875, to April 1, 1876, at 5%? For aulditional examples in interest, see page 253. PARTIAL PAYMENTS. 550. [DEMAND NOTE.] $ 470 Cincinnati, Jan. 1, 1874. For value received, I promise to pay to the order of Charles Gleason, Four Hundred Seventy i Dollars, on demand, with interest at 6 per cent. Ephraim Hint. 551. The above is the written promise of one person, Flint, to pay another person, Gleason, or any one to whom Gleason may order it paid, a certain sum of money, $ 470.60, for value received. Such a promise is called a promissory note, or simply a note. 552. The sum named in the note (as $ 470.60 above) is the face of the note. To discharge the interest and in part pay the above note a payment of $ 94.13 was made Nov: 1, 1874. What balance then remained due ? Ans. $ 400. Suppose the above balance of $ 400 to remain on interest from Nov. 1, 1874, to Nov. 1, 1875, when a payment of $ 224 was made, what sum then remained due ? Ans. $ 200. 553. Payments in part of a note or other debt, as the payments described above, are partial payments. 554. A record of the sum paid, with the date of the payment, is made upon the back of the note; such a record is an indorsement. The method adopted by the Supreme Court of the United States, and by most of the States, for computing interest in case of partial payments, requires (1.) That a payment be applied first to discharge accrued interest, and then, if the payment is large enough, to reduce the principal. (2.) That no unpaid interest be added to the principal to draw interest. |