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. = = 1yr. 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 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.

=

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 73 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?

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 interest of the same sum for

for any number of months is the 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?

845 mills

6 Od.

6d.

6 6d., Ans.

66. What is the interest of $345 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 16 yr.? 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.?

71. What is the interest of $412 for 5m.?

Ans. $10.30.

72. What is the interest of $42 for 2m. 22d.? Ans. $.574. 73. What is the interest of $54 for 22d.?

74. What is the interest of $2148 for 3m. 10d.?

Ans. $.198.

75. What is the interest of $75 for 1yr. 10m. 6d. ?

76. What is the interest of $173 for 1 yr. 8m. ?

244. In some States interest is allowed on the annual interest of the principal which is due and unpaid, if the note is written "with interest annually." Such examples may be solved by computing interest on the principal for the whole time and on each year's interest for the time it is due and unpaid; but the following brief practical mode of computing "annual interest" will be of service to the business man.

RULE. Find the interest on the principal for the given number of ENTIRE YEARS; on this interest find the interest for half of the years less one, and the months and days; and this latter interest is the EXCESS OF ANNUAL OVER SIMPLE INTEREST for the given time. To this excess add the interest on the principal for the whole time, and the sum is the annual interest for the given time. 77. What is the annual interest of $800 for 5 years?

$800, Principal.
.30

2 40.00

.12

2 8.80

240

Simple Int. of $1 for 5 years.

Simple Int. of $800 for 5 years. 5—1

= Simple Int. of $1 for 2yr. i. e. for =2yr.

2

Excess of annual over simple Int. of $800 for 3yr. = Simple Int. of the principal, as above.

$268.80 Annual Int. of $800 for 5yr., Ans.

78. What is the annual interest of $600 for 6yr. 4m. 18d?

SOLUTION. The interest of $600 for 6 years is $216; the interest of $216 for of (6—1) yr., increased by the months and days, viz. 2 yr. 4m. 18d., or 2yr. 10m. 18d. is $37.368, and this is the excess of the annual over the simple interest of $600 for 6yr. 4m. 18d. To this add the interest of $600 for 6yr. 4m. 18d., viz. $229.80, and we have $267.168, the annual int.

244. Rule for computing annual interest? Explain Ex. 77. Ex. 78

79. What is the annual interest of $462.84 for 7yr. 8m. 6d. ? Ans. $256.33.

80. What is the excess of annual over simple interest of $250 for 5yr. 7m. 24d.? Ans. $11.925.

81. What is the amount of $325, at annual interest for 8yr. 6m. 15d.? Ans. $529.393. 82. What is the amount of $4692.80, at annual interest for 9yr. 4m. 24d.?

PROBLEMS IN INTEREST.

245. In every example in interest there are four elements or particulars which claim special attention, viz. Principal, Rate, Time, and Interest, any three of which being given, the other can be found.

To find the Interest when the Principal, Rate, and Time are given, has, thus far, been the object of our discussion.

The other branches of the subject give rise to the following problems:

246. PROBLEM 1. given, to find the RATE.

Principal, Interest, and Time

Ex. 1. At what rate per cent. must $300 be put on interest to gain $18 in 2 years?

ANALYSIS. $300, at 1 per cent., will gain $6 in 2 years; .., to gain $18, the rate must be the quotient of $18÷ $6=3. Hence,

RULE. Divide the given interest by the interest of the principal, for the given time, at 1 per cent., and the quotient will be the

rate.

2. At what rate per cent. must $142 be put on interest to gain $21.30 in 3 years s? Ans. 5. 3. If $36 gain $7.56 in 3 years, what is the rate per cent.? 4. If $300 gain $43.80 in 2yr., what is the rate per cent.?

245. How many particulars claim attention in an example in interest? What are they? How many of them are given? 246. Object of Prob. 1?

Rule?