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Explanation.—When the months are not a single part of a year, that is, when the numerator is more than one, the most ready course is to take a number of months which will form a single part, as in the last question. Observe the same method when the days are not a single part of a month.
57. What is the interest of $1,07 for 2 years, 7 months and 9 days, at 44 per cent. ” Ans. $0,107-i-. 58. W gave his note June 15, 1823, for 1200 dol. lars, at 5 per cent. interest. The note was payable in 15 months from date; but W wishing to defer the ayment, agreed to add 24 per cent. to the rate of interest from the time the note was due until payment was made. What was the amount of the note May 2, 1826, when payment was made 2 Ans. $1421,75. 59. What is the interest on a note of $17,18, at 5 per cent., dated January 2, 1826, and paid February 25th, in the same year ! Ans. 0,126+.
As the exact interest is not found by the two preceding methods, we shall now examine a method by
which the interest may be found with a greater degree of accuracy. 60. What is the interest of $25,249 from January 1, 1825, to June 15, of the same year, at 5 per cent. ” 2 5, 2 4 9 , 0 5
6 5 0 , 5 7 3 1 5 2 3 0 Ans. $0,573-i-. Explanation.—The time is 5 months and 14 days, (not reckoning the day of settlement.). If we multiply 30 by the number of months, and add 14, the whole number of days thus found is 164, which is one day short of the true time. In most cases by adding 1 day for 2 months, the time will be found within 1 day,+always within 2 days, and frequently the exact time. By adding two days in this question, the time is 1 day too much, but the sum is so small that the error is but a little more than 2 mills. $1,26245 is the interest for 1 year, the interest for the given time must be ### of the same, therefore multiplying the interest for 1 year by 166, and dividing by 365, the quotient will be the interest required; but if we change ### to a decimal, we find,454 which is nearly equal to ###, consequently multiplying the interest for one year by ,454, and pointing off three more places of decimals, the product must be the same part of the interest for one year, that the multiplier is part of an unit or 1 year. (See Illustration, page 148.) - 61. What is the interest of $18 for 10 months, 23 days, at 4 per cent. The time is ### of a year. Ans. $0,646-1-.
62. What is the interest on a note of $96 for 2
years, 8 months, at 5 per cent. 2 Ans. $12,806. 63. What is the interest of 10 cents for 1 Y. 7 mo.
28 d. at 7 per cent.” Ans. 30,011 +. 64. What is the interest of $500 for 25 days, at 6 per cent.” Ans. $2,04.
65. At 12 per cent., what will be the interest of $40 for 1 month and 20 days? Ans. $0,657+.
66. What is the amount of $9 frem February 29, 1824, to December 23 of the same year, at 53 per cent. interest? Ans. $9,403+.
Note 7.—It will not be necessary generally, to carry the decimal of the days farther than to 3 places; but if greater accuracy be required, they may be carried to 4 or 5 places.
In the following 4 questions the exact time is
67. What is the interest on a note of $470,06, dated November 19, 1823, and paid June 16, 1826, at 6 per cent. 2
Explanation.—It is 2 years from November 19, 1823, to November 19, 1825. From November 19, 1825, to June 16, 1826, there are 209 days—counting 11 in Nov., 31 in Dec., 31 in Jan., 28 in Feb., 31 in March, 30 in April, 31 in May, and 16 in June. ,572 of a year equal 209 days, and 2,572 years is the multiplier, by which the interest for one year must be multiplied.
68. What is the interest of a note of $1100,50 dated October 21, 1824, and paid Sept. 20, 1826, at 44 per cent. ” Ans. $94,835+.
69. A gave his note of 725 dollars, August 21, 1824, to be on interest after 60 days, at 6 per eent. What was due on the note, Sept. 21, 1826?
70. What is the interest of $29 from May 3, 1824,
to July 4, 1825, at 5 # per cent.
Remark-We have explained 3 methods of finding interest, when the time comprises a part of a year.
The three following rules contain directions for finding interest, derived from those explanations.
When the rate is 6 per cent. for 1 year, find the per cent. for the given time by annexing # of the days contained in the odd month, (if any,) and the given days to half the even number of months, and multiply the principal by the same.
.Note 8.—When the per cent. is any other than 6, add or subtract # for every one the given per cent. is more or less than 6. If the per cent. be 5, subtract # ; if 4, #; if 7, add #, &c.
Multiply the interest for one year by the number of years, and add such a part of the interest for one year as the months and days are parts of a year.
.Note 9.—Parts of the interest for any number of years, may be taken for the interest of months and days, by observing what part ofthe number of years the months and days are.
Reduce all the time less than a year to the decimal of a year, and annex the decimal to the number of years; then multiply the interest for one year by the mixed number thus found, or by the decimal, if there be no years.
How to find the interest for days only, estimating the year at 360 days.
Estimating the year at 360 days agreeably to Note
6, Section 8, the per cent. for 6 days is 1 tenth of 1
per cent, that is, 1 mill, when the given rate is 6;
therefore, multiplying the principal by as many mills 19
as there are 6's in the number of days, gives the interest.
71. What is the interest of 22 dollars for 24 days, at 6 per cent.” Ans. 8 cents, 8 mills. 72. What is the interest of 57 dollars 24 cents for 27 days, at 6 per cent.” Ans. 25 cents 7+ mills. 73. What is the interest of $2,10 for 25 days, at 6 per cent. 2 Ans. $0,008+. 74. What is the interest of 10 dollars for 59 days, at 5 percent. ” Ans. 8 cents and 1 + mill.
To find the interest on notes when partial payments are made.
Cast the interest on the whole note from the date to the time a settlement is made, and add the interest to the principal. Then compute the interest on each endorsement from the time it was made to the time of settlement, and add the interest to the endorsement. Add the amount of all the endorsements together, and subtract the sum from the amount of the whole note, the remainder will show what is still due.*
75. A note of $137, was dated July 7, 1825, and paid June 14, 1826. January 2, 1826, an endorsement of $38 was made ; what was due when the note was paid, interest at 6 per cent. 2 Ans, $105,668+.
Illustration.—The design of the preceding rule is, that the partial payment or endorsement is to pay so much of the principal, and to stop the interest on an equal sum. By computing interest on the whole note after a part of it is paid, the interest computed on the part paid, is not due ; but by computing the interest upon an equal sum for the remaining time, and sub
* The interest in the examples under this rule is computed byRule 3d, page 221.