24. What is the interest of $375.31 for 3 months, at 6 per cent. ? 25. What is the interest of $60 for 7 months, at 8 per cent. ? What is the amount ? 26. What is the interest of $96 for 10 months, at 6 per cent. ? What is the amount ? 27. At 6 per cent., what is the interest of $600 for 1 day? Operation. 1 day is 3 of 30 days, or $600 Prin. a month; hence the interest .06 Rate. for 1 day will be 30. of the interest for 1 month. If, 12)$36.00 In. for 1 y 30)3.00 In. for 1 m. therefore, we find the inter est for 1 month, and take 3b Ans. $0.10 In. for 1 d. of this, it will evidently be the interest for 1 day. In like manner, any number of days may be considered a fractional part of a month, and the interest for them may be found in the same way Hence, 240. To compute the interest of any sum for a given number of days. First find the interest for 1 month as above, then take such a fractional part of 1 month's interest as is denoted by the given number of days. Thus for 1 day take o of 1 month's interest ; for 2 days, 3o, or 15 ; for 3 days, 30 or lo ; for 10 days, }; for 20 days, š; $c. 28. At 4 per cent., what is the interest of $470 for 10 days? Ans. $0.522. 29. What is the interest of $1000 for 1 y. I m. and 1 d., at 6 per cent. ? 30. What is the interest of $42.50 for 2 years and 6 months, at 7 per cent. ? 31. What is the interest of $69.46 for 1 year and 8 months, at 8 per cent. ? QUEST.-240. How is interest computed for days ? For 2 days, what part would you take ? For 5 days ? 7 days ? 12 days ? 25 days? 241. From the foregoing principles we may deduce the following GENERAL RULE FOR COMPUTING INTEREST. 1. FOR ONE YEAR. Multiply the principal by the given rate, and from the product point off as many figures for decimals, as there are decimal places in both factors. (Art. 237.) II. FOR TWO OR MORE YEARS. Multiply the interest of 1 year by the given number of years. (Art. 238.) III. FOR MONTHS. Take such a fractional part of 1 year's interest, as is denoted by the given number of months. (Art. 239.) IV. FOR DAYS. Take such a fractional part of 1 month's interest, as is denoted by the given number of days. Obs. 1. In calculating interest for months, a month, whether it contains 30 or 31 days, or even but 28 or 29, as in the case of February, is always assumed to be one twelfth of a year. 2. In calculating interest for days, 30 days are considered a month ; consequently the interest for 1 day, or any number of days under 30, is so many thirtieths of a month's interest. (Art. 170. Obs. 2.) This practice seems to have been originally adopted on account of its convenience. Though not strictly accurate, it is sanctioned by custom, and is everywhere allowed by law. 32. What is the interest of $45.23 for 1 year and 2 months, at 5 per cent. ? 33. What is the interest of $43.01 for 25 years, at 7 per cent. ? 34. What is the interest of $215.135 for 2 years and 3 months, at 6 per cent. ? 35. At 8 per cent., what is the interest of $75.98 for 3 years? 36. At 55 per cent., what is the interest of $939 for 4 years? 37. At 6 per cent., what is the interest of $137.50 for 6 months ? Quest.—241. What is the general rule for computing interest ? Obs. In reckoning interest, what part of a year is a month considered ? How many days are considered a month? Is this practice strictly accurate ? 38. At 7 per cent , what is the interest of $1500 for 10 days ? 39. At 20 per cent., what is the interest of $3000 for 3 days ? 40. At 125 per cent., what is the interest of $1736.25 for 6 months ? SECOND METHOD OF COMPUTING INTEREST. 242. There is another method of computing interest, which is very simple and convenient in its application, particularly when the interest is required for months and days at 6 per cent. INTEREST OF $1 FOR MONTHS. 66 66 .01; 3 is .015; 4 .02; 5 .025; .03; 243. We have seen, (Art. 237,) that, For 1 year, the interest of $1 is 6 cents, which is $.06; “ 1 month, “is is .005; “ 2 months, " is 2, or 3 of 6 cents, - 3 months, or of 6 cents, 66 4 months, “ is 12, or of 6 cents, - 5 months, “ is of 6 cents, “ “ 6 months, “ is 192, or 1 of 6 cents, That is, the interest of $1 for 1 month, at 6 per cent., is 5 mills; and for every 2 months, it is 1 cent, fc. Hence, 244. To find the interest of $1 for any number of months, at 6 per cent. Multiply the interest of $1 for 1 month, ($.005,) by the given number of months, and point off 3 decimal figures in the product. (Art. 191.) 1. At 6 per cent., what is the interest of $1 for 7 months ? Quest.—244. How may the interest of $1 be found for any number of months, at 6 per cent. ? 2. At 6 per cent., what is the interest of $1 for 8 months ? 3. At 6 per cent., what is the interest of $1 for 9 months ? For 10 months ? For 11 months ? 4. At 6 per cent., what is the interest of $1 for 14 months ? For 15 months ? For 18 months ? INTEREST OF $1 FOR DAYS. .002; .003; 66 66 245. Since the interest of $1 for 1 mo. (30 d.) is 5 mills, (Art. 243,) or $.005; For 6 days (} of 30 d.) the interest of $1 is } of 5 mills, or $.001; “ 12 days (of 30 d.) “ is of 5 mills, or “ 18 days (Š of 30 d.) “ is of 5 mills, or “24 days (of 30 d.) is of 5 mills, or .004; “ 3 days (1 of 30 d.) " is b of 5 mills, or .0005; That is, the interest of $1 for every 6 days, is 1 mill, or $.001; and for any number of days, it is as many mills, or thousandths of a dollar, as 6 is coniained times in the given number of days. Hence, 246. To find the interest of $1 for any number of days, at 6 per cent. Divide the given number of days by 6, and set the first quotient figure in thousandths' place, when the days are 6, or more than 6; but in ten thousandths' place, when they are less than 6. 5. What is the interest of $1 for 1 day, at 6 per cent. expressed decimally ? Ans. $.000166+ 6. What is the interest of $1 for 9 days, at 6 per cent. ? 22 days? 4 days? 14 days? 7. What is the interest of $1 for 10 days, at 6 per cent. ? 16 days ? 20 days ? 24 days? 27 days ? 28 days? 30 days? QUEST.–246. How may the interest of $1 be found for any number of days, at 6 per cent. ? 66 66 66 8. What is the interest of $1 for 1 year, 5 months, and 3 days, at 6 per cent. ? Solution. For 1 year, the interest of $1 is $.06 5 months, .025 3 days, .0005 $.0855 Ans. 9. What is the interest of $1 for 2 years, 7 months, and 20 days, at 6 per cent. ? 10. What is the interest of $1 for 3 years, 1 month, and 15 days, at 6 per cent. ? 11. What is the interest of $145 for 6 months and 24, days, at 6 per cent. ? Operation. The interest of $145 is 145 $145 Prin. times as much as the interest of .034 Int. of $1 for? $1 for the given time. We the time. therefore first find the interest 580 of $1 for the given time, which 435 is $.034; then multiply the $4.930 Ans. principal by it and point off 3 figures for decimals in the product. (Art. 191.) 247. From these illustrations we may derive a SECOND RULE FOR COMPUTING INTEREST. First find the interest of $1 for the given time, at 6 per cent. ; (Arts. 244, 6 ;) then multiply the principal by the interest of $1 for the time, and point off the product as before. (Art. 241.) Obs. 1. The interest at any other rate, greater, or less than 6 per cent. may be found by adding to, or subtracting from the interest at 6 per cent., such a fractional part of itself, as the required rate exceeds or falls short of 6 per cent. Thus, if the required rate is 7 per cent., first find the interest at 6 per cent., then add of it to itself ; if 5 per cent., subtract of it from itself, &c. 2. When it is required to compute the interest on a note, we must QUEST.—247. What is the second method of computing interest? Obs. When the rate per cent. is greater or less than 6 per cent., how proceed ? How compute the interest on a note ? |