402. The legal rates of interest, and the penalty for usury in the several States of the Union, are as follows: OBS. 1. On debts and judgments in favor of the United States, interest is computed at 6 per cent. 2. In Canada and Nova Scotia, the legal rate of interest is 6 per cent. In England and France it is 5 per cent.; in Ireland 6 per cent. In Italy, about the commencement of the 13th century, it varied from 20 to 30 per cent. a On tobacco contracts 8 per cent. b By contract as high as 10 per cent. c Bank interest 6 per cent.; conventional as high as 10 per cent. d By agreement as high as 12 per cent. e By agreement as high as 10 per cent. ƒ By agreement, any rate not exceeding 10 per cent. By contract as high as 12 per cent. h By agreement as high as 12 per cent. 403. Ex. 1. What is the interest of $30 for 1 year, at 6 per cent.? Analysis. We have seen that 6 per cent. is Tʊ; that is, $6 for $100, 6 cents for 100 cents, &c. (Art. 386.) Since therefore the interest of $1 (100 cents) for 1 year is 6 cents, the interest of $30 for the same time must be 30 times as much; and $30X.06 =$1.80. Ans. Operation. $30 Prin. .06 Rate. $1.80 Int. 1 yr. We first multiply the principal by the given rate per cent. expressed in decimals, as in percentage, and point off as many decimals in the product as there are decimal places in both factors. Ex. 2. What is the interest of $140.25 for 1 year, 1 month, and 10 days, at 7 per cent.? What is the amount? Operation. .07 Rate. 12)$9.8175 Int. 1 yr. 3) 8181 2727 66 1 mo. $10.9083 Interest. $140.25 Prin. added. $151.1583 Amount. 1 month is of a year; therefore the interest for 1 month is of 1 year's interest. 10 days are of 1 month, consequently the interest for 10 days, is of 1 month's interest. The amount is found by adding the principal and interest together. Note.-1. In adding the principal and interest, care must be taken to add dollars to dollars, cents to cents, &c. (Art. 374.) 2. When the rate per cent. is less than 10, a cipher must always be prefixed to the figure denoting it. (Art. 387. Obs. 1.) It is highly important that the principal and the rate should both be written correctly, in order to prevent mistakes in pointing off the product. Ex. 3. What is the interest of $250.80 for 4 years, at 5 per cent.? What is the amount? Solution.-$250.80X.05 $12.54, the interest for 1 year. Now $12.54X 4=$50.16, 66 4 years. And $250.80+$50.16 $300.96, the amount required. 404. From the foregoing illustrations and principles we deduce the following general RULE FOR COMPUTING INTEREST. I. 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. 324.) II. FOR TWO OR MORE YEARS. by the given number of years. III. FOR MONTHS. Multiply the interest of 1 year Take such a fractional part of 1 year's in terest, as is denoted by the given number of months. IV. FOR DAYS. Take such a fractional part of one month's interest, as is denoted by the given number of days. The amount is found by adding the principal and interest together. OBS. 1. The reason of this rule is evident from the consideration that the given rate per cent. per annum denotes hundredths. (Arts. 386, 398.) Now when the rate is 6 per cent. we multiply by .06, when 7 per cent. by .07, &c., and point off two figures in the product; consequently the result will be the same as to multiply by TT, &c. 2. In calculating interest, a month, whether it contains 30 or 31 days, or even but 28 or 29, as in the case of February, is assumed to be one twelfth of a year. Therefore, for 1 month we take of 1 year's interest; for 2 months, ; for 3 months, ; for 4 months, ; for 6 months, ; for 8 months,, &c. Again, 30 days are commonly 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. 303. Obs. 2.) Therefore, for 1 day we take of 1 month's interest; for 2 days, 1; for 3 days, '; for 5 days, ; for 10 days,, &c. This practice seems to have been originally adopted on account of its convenience. Though not strictly accurate, it is sanctioned by general usage. 3. Allowing 30 days to a month, and 12 months to a year, a year would contain only 360 days, which in point of fact is 35, or less than an ordinary year. Hence, To find the interest for any number of days with entire accuracy, we must take so many 365ths of 1 year's interest, as is denoted by the given number of days; or, find the interest for the days as above; from this subtract of QUEST.-404. How is interest computed for a year? How for any number of years? How for months? How for days? How find the amount? Obs. In reckoning interest, what part of a year is a month considered? How many days are commonly considered a month? Is this practice accurate? itself, and the remainder will be the exact interest. The laws of New York, and several other states, require this deduction to be made. In business, when the mills in the result are 5, or over, it is customary to add 1 to the cents; if under 5, to disregard them. EXAMPLES. per cent.? per cent.? mo., at 6 per cent.? 1. What is the interest of $423 for 1 yr., at 7 per cent. ? 2. What is the interest of $240.31 for 3 yrs., at 6 per cent.? 3. What is the interest of $403.67 for 2 yrs., at 5 per cent.? 4. What is the interest of $640 for 1 yr., at 8 per cent.? 5. What is the interest of $430.45 for 2 yrs., at 7 per cent.? 6. What is the interest of $185.06 for 4 yrs., at 6 per cent.? 7. What is the interest of $864.80 for 5 yrs., at 4 8. What is the interest of $763 for 4 months, at 7 9. What is the interest of $940.20 for 10. What is the interest of $243.10 for 5 mo., at 8 per cent.? 11. What is the interest of $195.82 for 7 mo., at 6 per cent.? 12. What is the interest of $425.35 for 9 mo., at 6 per cent.? 13. At 7 per cent., what is the int. of $738 for 1 yr. and 2 mo. ? 14. At 6 per cent., what is the int. of $894 for 1 yr. and 8 mo. ? 15. At 7 per cent., what is the amount of $926 for 6 mo. ? 16. At 7 per cent., what is the amt. of $648 for 2 mo. 15 d. ? 17. At 6 per cent., what is the amt. of $1000 for 1 mo. 11 d.? 18. At 5 per cent., what is the amt. of $1565.45 for 3 mo. ? 19. At 6 per cent., what is the amt. of $872 for 4 mo.? 20. What is the int. of $681 for 10 days, at 6 per cent.? 21. What is the int. of $483.26 for 15 d., at 7 per cent.? 22. What is the int. of $569.40 for 20 d., at 6 per cent.? 23. What is the amt. of $95 for 1 yr. and 6 mo., at 5 per cent.? 24. What is the amt. of $148 for 8 mo. 12 d., at 6 per cent.? 25. What is the amt. of $700 for 30 d., at 7 per cent.? 26. What is the int. of $340 for 60 d., at 54 per cent.? 27. What is the int. of $4685 for 90 d., at 64 per cent.? 28. What is the amt. of $3293 for 30 d., at 7 per cent.? 29. What is the amt. of $5265 for 15 d., at 6 per cent.? 30. What is the int. of $8310 for 10 d., at 7 per cent.? 31. What is the int. of $50625 for 21 d., at 6 per cent.? 82. What is the amt. of $65256 for 4 mo., at 7 per cent.? SECOND METHOD OF COMPUTING INTEREST. 405. 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. 406. We have seen that for 1 year, the interest of $1 at 6 per cent. is 6 cents., or $.06; (Art. 404;) therefore, Hence, The interest of $1 for 1 month, at 6 per cent., is 5 mills, for every 2 months, it is 1 cent; and for any number of months, it is as many cents, or hundredths of a dollar, as 2 is contained times in the given number of months. 407. Since the interest of $1 for 1 month (30 days) is 5 mills, 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 contained times in the given number of days. 408. Hence, 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. OBS. For 60 days (2 mo.) the interest of $1 is 1 cent; (Art. 406;) when, therefore, the number of days is 60 or over, the first quotient figure must Dccupy hundredths' place. QUEST.-408. How find the interest of $1 for any number of days, at 6 per cent.? |