54.

$167.42.

Providence, April 15, 1858. For value received, I promise to pay A. B., or order, one hundred sixty-seven and dollars, in six months from date, with interest. C. D.

INDORSEMENTS: May 21, 1859, $42.18; July 17, 1860, $6.25; Sept. 9, 1860, $48.16; Jan. 27, 1861, $27.47; what was due April 15, 1862? Ans. $72.072.

55. $472.76.

New York, June 4, 1860.

For value received of Walter Willis, I promise to pay him, or his order, four hundred seventy-two dollars and seventy-six cents, in six months from date, with interest at 7 per cent. afterwards. SAMUEL JOHNSON. INDORSEMENTS: April 10, 1861, $125.843; Nov. 28, 1861. $133.724; April 15, 1862, $223.081; what was due Nov. 13, 1862 ? Ans. $24.97. 239. The following is a common rule when settlement is made within a year after interest commences.

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.

57. $387.75.

Burlington, Vt., May 15, 1861. For value received, I promise to pay to Samuel Adams, on demand, three hundred eighty-seven and 7% dollars, with inter10% est 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 ? Ans. $152.186.

58. A note of $2500, dated June 4, 1861, has the following INDORSEMENTS: Sept. 4, 1861, $562.50; Dec. 24, 1861, $846.37; Feb. 18, 1862, $362.63; what was due May 12, 1862? Ans. $821.539.

239. Rule when settlement is made within a year.

* 239.

The following is THE CONNECTICUT RULE:

1. When payments are made one year or more from the time from which the interest is reckoned, or when any payment is less than the interest then due, the work of computing the interest is performed according to THE UNITED STATES RULE.

2. When payments exceeding the interest then due, are made within a year from the time from which the interest is reckoned, the amount of the principal must be found for a full year, and the amount of the payment from the time of payment to the end of such full year, and this, deducted from the amount of the principal previously obtained, will form the new principal.

3. If the year extends beyond the time of settlement, interest on the payment is computed to the time of settlement.

*58. $975.00. New Haven, January 3, 1863. For value received, I promise to pay John Sherman, or order, nine hundred and seventy-five dollars, on demand, with interest. RICHARD THORPE.

INDORSEMENTS: March 5, 1864, $150: July 6, 1864, $225.75; July 1, 1866, $25; what was due on settlement, Oct. 31, 1866?

OPERATION.

$975.00 Principal.

68.575 Interest to March 5, 1864.

1043.575 Amount of Principal to March 5, 1864.

150.00 1st Payment.

893.575 2d Principal.

5 3.614 Interest for 1 year from March 5, 1864. 947.189 Amount of 2d Principal from March 5, 1864. 225.75 2d Payment.

8.992 Int. on 2d Payment to March 5, 1865. 234.742 Amount of 2d Payment to March 5, 1865. 712.447 2d Remainder for 3d Principal.

66

66

66

66

66

70.772 Interest to time of settlement, Oct. 31, 1866. 783.219 Amount 66 25.000 3d Payment, less than the Interest then due. $758.219 Due on settlement, Oct. 31, 1866, Ans.

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?

SOLUTION.

Amount of Principal to July 25, '60, 1 yr.,

$1590.

1st Payment,

$100.

Int. of 1st Pay't to July 25, '60, 10 m. 12 d.,

5.20

2d Remainder or 3d Principal,

750.723

Int. of 3 d Prin. to June 13, '62, 10 m. 18 d.,

39.788

Sum due at settlement, June 13, '62, Ans.,

315. $475.511

240. Third rule for computing interest on notes?

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 simple than the foregoing.

The following method of reckoning interest is largely used by business

men.

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

1 yr.

8 m. is 1 dime. is $1.

241. The interest of $1 for 6 days, at 6 per cent., is 1 mill. The interest of $1 for ten times 6 d.: 60 d. 2 m. is 1 cent. The interest of $1 for ten times 2 m.) = 20 m. 1: The interest of $1 for ten times 20m.16 yr. 8 m. 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 multiples and aliquot parts of these results as the given time may 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.

73

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. e. for 36873 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? $7.20: Int. for 2 m. 21.60 Int. for 6 m.

=

= 3 times 2 m.

$25.5 6 Int. for 7 m. 3 d., Ans.

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=7.1 m.=7 m. 3 d., 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? Note 2?