Interest.* 507. This is a percentage paid for the use or retention of money. When no time is specified, one year is understood. Thus, when we say 5 p. c., the words per annum, by the year, are understood. The sum on which interest is paid is called the principal. The interest of 100, for one year, is called the rate, and the sum of principal and interest, the amount. Interest is usually regulated by law,† and varies considerably in different countries, according to the abundance or scarcity of money, facilities of trade, &c. Ex. 1. Suppose we would have the interest of $1776 for one year, at 6 p. c. The question here evidently is, if $100 gain $6, what, will $1776 gain? Consequently, we have the proportion $100 $1776 $6 $106,56. Answer. Hence the general rule: Multiply the principal by the rate p. c., and divide by 100. Or, as the question (498) evidently requires nothing more than 6 p. c. of $1776, we multiply by ,06, thus: $1776,06 $106,56, as before. That is, multiply the principal by the rate considered as hundredths. 508. If we require the interest for 2, 3, 4, 5, 6, &c. years, it is plain that we have only to multiply $106,56, which is the interest for one year, by 2, 3, 4, 5, 6, &c. Or, we may multiply the rate by the number of years, (419,) and proceed as before. Suppose we would have the interest of $1776 for 31 years, at 6 p. c., we say, ,06 × 31,21; then, $1776,21= $272,96. Proof. $106,56 × 31 = $53,28 × 7=$372,96. "In the New England States, New Jersey, Pennsylvania, Delaware, Maryland, Virginia, North Carolina, Tennessee, Kentucky, Ohio, Indiana, Illinois, Missouri, Arkansas, and the Dist. of Columbia, and on U. S. Notes, the rate is 6 p. c. In New York, S. Carolina, Michigan, Wisconsin, and Iowa, it is 7 p. c. In Georgia, Alabama, Mississippi, and Florida, 8 p. c. In Louisiana, 5 p. c. though the bank interest is ,06, and conventional interest may be as high as,10. In Maryland the interest on tobacco contracts is,08. In Mississippi, Missouri, and Arkansas, the interest by agreement may be as high as,10, and in Illinois, Wisconsin, and Iowa, as high as,12."-Chase's Arith.,.page 66. † In England, legal interest is 5 p. c. 509. Suppose we would have the int. for months, say 8 mos.; the proportion is then compound, and becomes $100 $1776: $6:$71,04 2 4 half the number of months, which divided by 100 is,04. Hence we see that the int. at 6 p. c. for any number of months is found in multiplying the principal by half the number of months, considered as hundredths. The following table shows the number of days from the beginning of the year to the first of each respective month: 0 1 mo. (Jan.) 5 mo. (May) 120 9 mo. (Sept.) 243 10 mo. (Oct.) 273 11 mo. (Nov.) 304 12 mo. (Dec.) 334 By this table we easily find the number of days from any day of one month to any day of another. Rule: Find the difference between the numbers opposite the given months, under which write the difference between the given dates, and when the first date is the smaller number, add; when it is the greater, subtract. To the result add 1, when the second month of leap-year is included between the given dates. When the last date is in the following year, reverse the or der of the dates, proceed as above, and subtract the result from 365. The remainder is the required number. Also, to this remainder add 1, when the second month of leap-year is included between the given dates. 1. Required the number of days from 4 mo. 12 to 12 mo. 25? 244 No. of days from 4 mo. 1 to 12 mo. 1. = 13 diff. of dates added. 257 Answer. 2. What is the number of days from Apr. 25 to Dec. 12? Ans. 231. 3. Required the number of days from 12 mo. 25, 1853, to 4 mo. 12, 1854 ? Ans. 108. 4. Required the number of days from 12 mo. 12, 1855, to 4 mo. 25, 1856 ? Ans. 135. 510. As ,06 is the int. of 100 for one year at 6 p. c., 12 of = ,001 is the ,06,005 is the int. for 1 mo.; and of,005 18 int. for of 1 mo. or 6 days. Consequently, the int. for any number n of days 6:n::,001; multiplying (413) the first and third terms by 1000, we have 6000:n :: 1 have the following rule, called the bank rule: n 6000 Hence we To find the int. at 6 p. c. for any number of days, multiply the principal by the number of days, and divide by 6000. Ex. 1. Suppose we would have the int. of $1776 for 24 1776 X 24 6000 days, we say, = 1,776 X 4 $7,104. Answer. To find the Simple Interest of any amount for years, months. and days: Reduce the years and months to months, place the number of days on the right, and multiply the result, considered as mills,by half the principal, or half the result by the whole principal. 2 Examples. 1. Required the interest of $625 for 2 yrs. 9 mo. 21 d. yrs. 9 mo. = 33 mo. 213=7; then 337 × 3121 105312 m. = $105,314. Or, ,1685 × 625 1685 16 $105,314, (273.) 21 d. 7 Elucidation. = = mo.= 10 mo.; consequently, these tenths have their true value when placed on the right of 33 mo. Then 100 625:6 Now the rate 6 p. c. measures the con12:33,7 stant divisor 12 and the result is 2. Also the term 337 tenths, divided by the constant divisor 100, becomes 337 thousandths or mills, hence the rule. 2. What is the int. of $1337,67 for 3 yrs. 5 mo. 17 d. ? 3 yrs. 5 mo. 17 d. ÷ 100 =,4153 mo. ;-then half the principal 668,835,4153 $278,01,483. Or 222,945 X 1,247 $278,01 +. 3. What is the int. of £68 15 s. 8 d. for 4 yrs. 3 mo. 19 d.? £68 15 s. 8 d. 68,781,: then ,5161 34,391 11,46,7= £17,7575638 £17 15 s. 12 d. +. = 511. As the int. at 6 p. c. is found with great facility, the int. at any other rate may be found by Practice. Thus, for the int. of $1776 at 4 p. c., we say 3 p. c. is 1) 106,56 int. at 6 p. c. 11" is)53,28 26,64 $79,92 or, by complement, $106,56 for 1 p. c. subtr. 1 2. What is the int. of $236,14 at 6 p. c.? 26,64 $79,92. Ans. $14,17-. 3. What is the int. of $993,60, at 4 p. c.? 4. What is the int. of £294 16 s. 8 d. at 5 Ans. $44,71. p. c.? Ans. £14 14 s. 10 d. Ans. £63. p. c.? 5. What is the int. of $900 at 7 7. What is the int. of $169, for 7 mo. at 6 $1,69 × 31 8. What is the int. of $2600, for 3 yrs. = Ans. $285,18. p. c.? Ans. $5,911. 7 mo. and 5d. at $26X21 Ans. $561,163. 9. What is the int. of £65 13 s. 4 d., for 78 days at 6 p. c. ,065613 Ans. 17 s. 03 d. 10. What does £786 16 s. amount to in 4 yrs. 8 mo. 6 p. c.? = ? Then £786 16 s. + £222 5 s. 5 d. 1 s. 5 d. +. 512. To find in what time a sum at simple int. will double itself—that is, in how many years the whole amount of int. will equal the principal-divide 100 by the rate p. c. 1. Suppose we would find in what time the int. of $350 will amount to $350, at 6 p. c., we say Cap. Cap. $ $ 100 Int. 350 :: 6 : 21, one year's int. 163 yrs. Answer. hence the rule, according to which a sum at 7 p. c. will double itself in 14 years, at 8 p. c. in 123 yrs., at 9 p. c. in 11 yrs. &c. 513. To find in what time the int. of a given sum will attain any other given amount: Divide the given amount by the int. of the given sum for one year at the given rate. 2. In what time will the int. of $350 amount to $200 at 6 p. c.? 21 : 200 :: 1: 911 yrs. Ans. Hence the rule. SECTION XXV. PARTIAL PAYMENTS DISCOUNT- INSURANCE -DUTIES TARE-TAX-GENERAL AVERAGE. Partial Payments. 514. WHEN these payments, which are made at sundry times to cancel a Promissory Note, or other obligation, are, with their respective dates, entered on the back of such instruments, they are called endorsements. When a final settlement is made within one year from the date of the instrument, it is customary to calculate the interest on the whole from the time of its date, or from the time it becomes due, to the time of settlement; and on each endorsement, from its date, in like manner. Then the amount of all the endorsements, with their several interests, is subtracted from that of the principal and its interest, and the remainder is the balance due. $500. PORTLAND, Mar. 10, 1853. For value received, I promise to pay Rufus Horton, or order, five hundred dollars, on demand, with interest. NOBLE H. HEATH. Endorsements.-June 5, 1853, received $60. July 20, 1853, received $95. Sept. 19, 1853, received $100. Nov. 23, 1853, received $40. What is due Mar. 10, 1854? Amount of $500 for 1 yr. $530,00. Int. of $60 for 9 mo. 5 d.....$2,75 $295,00 9,88 $304,88 957 mo. 18 d..... 3,61 Balance due Mar. 10, 1854, $225,12. GORHAM, Jan. 4, 1853. For value received, I promise to pay John Horton, or order, one thousand, two hundred and sixty dollars, on demand, with interest. PHILIP HEATH. $1260. Endorsements.-Mar. 15, 1853, received $200. June 9, |