SIMPLE INTEREST. DEFINITION.-Interest is a premium paid to the lend. er, by the borrower, for the use of money lent. Simple Interest is reckoned at 6 por cent. that is, at the rate of 6 dolls. for the use of 100 dolls. one year; and so in proportion for a longer, or shorter time, or for a smaller, or larger sum. Principal is the money lent. Rate per cent. is the price agreed on. The amount is the principal and interest together, CASE I. The principal and rate given, to find the interest for one year, or more, &c. RULE,–Multiply the principal by the rate per cent. and that product by the number of years, the last, product pointed, according to the rule of decimals, will be the answer for that time, in dollars and parts of dollars, Examples. 1, What is the interest of $22.16 cents for one year, at 6 5 per cent, per apnum? do!s, cts. 06 rate per eent. 1.3296 I time $1•3296 = $1•32.91 Answer. Nare.-Six per cent. must be written •06 and seven per cent. should be written •07, &e. this being observed, the rule of dec inal fractions exactly applies. 2. What is the interest of $223:14 cts. for 5 years, aç 5 per cent. per annum? D. cts. m. $223.14 x•06 = 13.38 84X5 — 66.94.2t Ans. 3. What is the interest of 123 dols. 10 cts. I mill, for 7 years, at 9 per cent. per annum ? yrs. Ans $77.55.37 CASE II. When the amount is required. RULE.Find the interest as in case first, and to it add. the principal, the sum is the amount. Examples. 1. What will 810:15 cts. amount to in 12 years, at 6 per cent. per annum? 810.15 06 .6090 12 7.3080 interest. 10.15 principal added. Ans. $17.4580 amount. 2. What is the amount of 81.12 cts. for 12 years, at 12: per cent. per annum? Ans. 82.73-21 3. What is the amount of $242.17 čts. for 3 years, at 9 per cento per annum ? Ans. 8307-55-51. CASE III. When there are years, months and days in the time. RULE '1st. Reduce the days and months to the decia mal of a year, then multiply the principal, rate, and time together, the product pointed for decimals according to rule will be the answer. Rule 2d. Find the interest for the years by case first; for the months, divide a year's interest by the aliquot parts of a year; and for the days, divide a month's interest by the aliquot parts of a month; the several quotients added with the interest for the years will be the Examples 1. What is the interest of 86:22 cts. for 2 years, hi months, 10 days, at 6 per cent. per annum? answer. years mo. days years 6 10 D. cts, cts. m. 94.3.7 Ans. The same question by rule second. 86.22 principal. 06 rate. 6 mo. = of a year. 1):3732 1 year's interest. 2 7464 2 year's interest. •0103f 10 day's interest. Ans, .9433t interest for 2 yr.6 mo.10ds. 2. What is the interest of $10:10 cts, for 10 years, il months, at 9 per cent. ? C. m. years. mo, years. D, c. 10.10 09 6 mo. 31 of 1 year. 1)-9090 1 year's interest, 10 9.0300 10 yrs, interest. 3)0.2272t 3 months' interest, D. ci m. $9.9232+ Ans. 9.92.3f. 3. What is the interest of $213.23 cts. for 3 years, 12 days, at 10 per cent. ? Ans. $64.67 cts. :9tm. The same question by rule second, Ans. $64-67 cts. 9tm. 4. What is the interest of $23.23 cts for 1 year 9 mo. at 6 per cent. ? Ans. $2.43 cts. 97 m. The same question by rule second, Ans. $2.43 cts. 9 m. 5. What is the interest of 8121•11 cts. for 2 years, 7 mo, at 5 per cent. ? Ans. S 15:64 cts, 37 m. The same question by rule second. Ans, $15.64 cts, 37 m. Note. In the preceding examples I have considered 30 days a month, and 12 months' a year; which is the general method of casting interest; but by this method 5 days are lost in a year; 12x305360 days ; which in large sums would amount to something worthy of potice. CASE IV. hundred sixty five days to a year. Rule.--Reduce the given number of days to the decimal of a year, which contains 365 days; then multiply the principal, rate, and time together, point off for decimals according to the rule of decimal fractions, and the product is the answer. Examples. 1. What is the interest of 821.20 cts. for 27 days, at 9 per cent. per annum? 27 days is = •0739 $21•20 X 09 X •0739 14 cts. I fmill-Ans. 2. What is the interest of $12:06, for 3 years 141 days at 6 per cent. per annum? Ans. 82.451 3. What is the interest of $3.03, for 138 days, at 6 per cent. per annum ? Ans, :06 cts, 77 m. CASE V. 19 When the time is months, and the rate per cent. is six. RULE. Multiply the principal by half the number of months, (which is just equal to the rate for the time when the annual rate per cent. is six) if the months are odd, annex :5 to the right hand, the product is the interest for the tiine. Examples. 1. What is the interest of 21 dollars for 10 months, at 6 per cent. per annum? 10 months •05X821.31:05 cts. Ans. 2. What is the interest of 250 dollars 11 cents, for 16 months, at 6 per cent. per annum? Ans. $20.00 ctş. 87 m.. 3. What is the interest of $121.12 cents, for 21 months, at 6 per cent. per annum ? Ans. $12.71 cts. 77 m. 4. What is the interest of 9 dollars, 9 cents, for 9 months, at 6 per cent. per annum? Ans. •40 cts. 97 m. CASE VI. When the time is mo th8, and the rate any other than six, RULE. Find the rate for the time by proportion; say, as twelve months is to the rate per annum, so is the given number of months to the rate for the time. Examples. 1. What is the interest of $26.21 cts, for 8 months, at 9 per centper annum? Months. Per cent. Months. 8 : 6 the rate for that time. $26•21 X •06 rate=$1.57.2 Ans. 2. What is the interest of $12:11 cts. for 21 months, at 11 per cent. per annum? Ans. $2.33•17 m. 3. What is the interest of 111 dols. for 13 months at ten per cent. per annum ? Ans. $12:025 4. What is the interest of 819 for 22 months, at 12 per cent. per annum ? Ans. 84:18 cts. As 12 : 9 : : CASE VII. When endorsements are made on notes, &C. RULE 1. Find the amount of the note to the end of the first year ; and find also the amount of all the endorsements (made in that year,) and subtract the amount of the endorsements from the amount of the note, the remainder will be a principal for the secfond year; thus proceed from year to year ; the last principal 'thus found will be what is due on final by this method the endorsements are applied to keep down the interest. settlement : |