RULE. 1. Find the amount of the principal from the time when interest commenced to the time of settlement.

2. Find the interest of each payment from the time of payment to the time of settlement.

3. Subtract the sum of the payments with their interest from the amount of the principal.

NOTE. The above rule is often used whatever may be the time; but for long periods it is manifestly unjust, for by it the debtor, by merely paying interest annually at 6 per cent., will in less than 24 years cancel his entire debt, and not only so, the person who loans the money will actually become indebted to the one who borrows.

57. $387.75.

Boston, May 15, 1861.

For value received, I promise to pay to Samuel Adams, on demand, three hundred eighty-seven and dollars, with interest from date. HENRY PHILLIPS.

INDORSEMENTS: July 21, 1861, $75; Oct. 10, 1861, $125; Feb. 24, 1862, $50; what was due at the time of settlement, May 15, 1862?

4.479

5 0.

0.67 5

2.5 8.8 29

$152.186

Int. of 2d Payment from Oct. 10, 7m. 5d., 3d Payment,

Int. of 3d Payment from Feb. 24, 2m. 21d.,

Sum of Payments, with their Interest,

Sum due May 15, 1862, Ans.,

58. A note of $2500, dated June 4, 1861, has the foll

INDORSEMENTS: Sept. 4, 1861, $562.50; Dec. 2 $846.37; Feb. 18, 1862, $362.63; what was due 1862?

Ans.

239. Is this rule just for long periods of time? Wh

240. Many business men, in computing the interest on notes, adopt the following

RULE. Find the interest of the principal for a year; also of each payment made during the year from the time of payment to the end of the year. Then subtract the sum of the payments, together with their interest, from the amount of the principal, and. the remainder is a new principal, with which proceed for another year, and so on to the time of settlement.

59. A note of $1500, dated July 25, 1859, has the following INDORSEMENTS: Sept. 13, 1859, $100; Jan. 25, 1860, $300; Sept. 19, 1860, $250; Dec. 25, 1860, $225; Aug. 13, 1861, $300; what was due June 13, 1862?

60. A note of $684, dated May 25, 1859, has the following

INDORSEMENTS: June 1, 1859, $100; July 7, 1860, $100; Oct. 13, 1860, $75; Dec. 19, 1860, $50;, June 7, 1861, $100; Aug. 13, 1861, $40; what was due July 15, 1862?

Ans. $302.044.

NOTE. There is, perhaps, no other operation in Practical Arithmetic in which accountants differ so much as in the mode of computing interest. All the methods are based upon the principles developed in the preceding pages, and it is believed there is no plan, universally applicable, which is more brief and simple than the foregoing. The solution may usually, however, be much shortened, as in the following Articles.

The principal advantage arises from the best divisions of time. Facility in making the best divisions can be easily acquired by practice, and to one having frequent occasion to compute interest the attainment is of great importance.

241. The interest of $1 for 6 days, at 6 per cent., is 1 mill. The interest of $1 for ten times 6d. 60d. = 2m. is 1 cent. The interest of $1 for ten times 2m. 20m.: lyr. 8m. is 1 dime. The interest of $1 for ten times 20m. 16yr. 8m. is $1. So the interest of $2, $3, or $1000, for the same times, is 2, 3, or 1000 mills, cents, dimes, or dollars. Thus we see that any number of dollars expresses its own interest in mills, cents, dimes, or dollars for the above-mentioned times, and hence, to know the interest it is only necessary to determine the place of the decimal point.

61. What is the interest of $324 for 93 days?

242. To compute interest at 6 per cent. for months and days,

RULE. Move the decimal point in the principal two places to

240. What of different modes of computing interest? What of the best division of time? 241. Any sum of money expresses its own interest at six per cent. for what times?

ward the left, and the result will be the interest for TWO MONTHS or SIXTY DAYS. Move the point three places toward the left, and the result will be the interest for SIX DAYS. Then take such mul tiples and aliquot parts of these results as the given time mag require, and the sum of these will be the interest.

PROOF. Divide the computed interest by the interest of the principal for one month, and the quotient should be the number of months expressed in the example; or, divide by the interest for one day, and the quotient should be the number of days.

NOTE 1. This is the most simple mode of proof, and applies to all rules for computing interest. The Problems in Interest, page 203, furnish other methods of proof.

NOTE 2. In computing interest it is customary to consider 30 days a month and 12 months a year, and .. the computed interest for 12 times 30 days, or 360 days (i. c. for 388 = of a year), is truly the interest for a whole year. Thus, the computed interest for any number of days is too large and it must.. be diminished by of itself to find the true interest. As interest is usually computed for months and days the difference is slight, and, in course of business, is seldom considered; but in England, and in dealing with the United States Government, it is customary to compute true interest.

62. What is the interest of $720 for 7 months and 3 days?

PROOF. The interest of the principal for 1 month is $3.60, and the Ans. to the example is $25.56; .. the time in months is $25.56 $3.60 = 7.1m. =7m. 3d., the time given in the example.

63. What is the interest of $1260 for 75 days?

242. Rule for computing interest for months and days, at 6 per cent.? Proof

Note 1? Note 2?

243. Three days is of a month, .. of the interest of $1, or any other sum, for 1 month, is the interest of the same sum for 3 days. In like manner, of the interest of any sum for any number of months is the interest of the same sum for three times as many days.

64. What is the interest of $765 for 2m. 6d.?

65. What is the interest of $845 for 6 days?

6 Od.

6d.

6 6d., Ans.

845 mills=

66. What is the interest of $845 for 2 months?

$.845, Ans.

845 cents $8.45, Ans.

67. What is the interest of $845 for lyr. 8m.?

Ten times 845 cents= $84.50, Ans.

68. What is the interest of $845 for 163yr.?

Ten times $84.50 = $845, Ans.

NOTE. The pupil will observe that merely changing the position of the decimal point, as in the four preceding examples, gives the interest of any sum for 6 days, for 2 months, for 1 year and 8 months, or for 16} years.

69. What is the interest of $845 for 1yr. 10m. 6d.?

70. What is the interest of $348 for 22 days?

244. One tenth of the interest of any sum for any number of months, is the interest of the same sum for how many days? Rule for determining the interest of any sum for 6 days? For 2 months? For lyr. 8m.? For 16yr. 8m.?