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FIRST OPERATION.

SECOND OPERATION.

Having found the Principal,

$8 4.5 0

interest for 1 year, Rate per cent.

.07

and then for 2 years,

the interest for 5 Interest for 1 year,

5.9 1 5 0

months is obtained 2

by first taking of Int. for 2

1 1.8 3 0 0

1 year's interest, years,

for 4 months, and Int. for 4mo., or 4 of 1yr. 1.9 7 1 6

then 1 of this last Int. for 1mo., or of 4mo. .4 92 9+ interest for 1 month. Int. for 10d., or of 1mo. .1 6 43+ And since 10 days Int. for 2d., or of 10d. .0 3 2 8+

are } of 1 month, Int. for 2yr. 5mo. 12d. $ 1 4.4 9 16+ Ans. month's interest for

we take of 1

the interest of 10 days; and since 2 days are } of 10 days, we take of the last interest for 2 days. The interest as found for the several parts of the whole time, added together, gives the interest required.

We first find the inPrincipal,

$8 4.50 terest on the given sum Int. of $1 at 6 per cent.

.1 47 at 6 per cent., and then

add to this interest the 5 9 150

fractional part of itself, 3 3800

denoted by the excess 8 4 5 0

of the rate above 6 per

cent. This excess is 1 Int. at 6 per cent. 1 2.4 2 150

per cent.; therefore we of int. at 6 per cent. 2.0 7 0 2 5

add i of the interest at Int. at 7 per cent. $ 1 4.4 917 5 Ans. 6 per cent. to that in

terest for the answer. If the rate per cent. had been less than 6 per cent, we should have subtracted the fractional part.

Rule 1.— First find the interest for one year by multiplying the principal by the rate per cent. expressed decimally ; and for two or more years multiply this product by the number of years.

Find the interest for months by taking the most convenient fractional part or parts of ONE year's interest.

Find the interest for days by taking the most convenient fractional part or parts of ONE month's interest. Or,

RULE 2. Find the interest of the given sum at 6 per cent., and then add to this interest, or subtract from it, such a fractional part of itself as the given rate is greater or less than 6 per cent.

Note 1. - < of the interest at 6 per cent. may be taken for that at 1 per cent.; Į, for that at 1} per cent.; }, for that at 2 per cent.; d, for that at 3 per

From the interest at 6 per cent. may be taken of itself for that at 4 per cent. ; $ of itself for that at 4 per cent.; and ( of itself for that at 5 per cent. To the interest at 6 per cent. may be added of itself for that at 7 per

cent.

cent. ; # of itself for that at 74 per cent. ; $ of itself for that at 8 per cent ; and s of itself for that at 9 per cent. If the rate is 12 per cent., the interest at 6 per cent. may be taken twice; if 18 per cent., the interest at 6 per cent. may be taken three times, etc.

NOTE 2. · When in this book tho rate of interest is not given, 6 per cent. is to be understood.

EXAMPLES.

2. What is the interest of $ 16.75 for 7 months and 17 days, at 7 per cent. ?

Ans. $ 0.739. 3. What is the interest of $ 11.104 from April 17, 1852, to December 7, 1852, at 7 per

cent. ?

Ans. $ 0.496. 4. What is the interest of $ 12.69, from January 2, 1853, to August 30, 1854, at 7 per cent. ?

Ans. $1.471. 5. What is the interest of $ 5000 for 2 years 5 months 26 days, at 7 per cent. ?

6. What is the amount of $ 416 for 3 years 16 days, at 7 per cent. ?

Ans. $ 504.64. 7. What is the interest of $ 336 for 15 days, at 5 per cent. ?

Ans. $ 0.70. 8. What is the interest of $ 17869.75 from February 7, 1852, to January 11, 1860, at 5 per cent. ?

Ans. $ 7083.3703. 9. What is the interest of $ 300.50 for 1 year 2 months and 15 days?

Ans. $ 21.786. 10. What is the interest of $ 37 for 29 days, at 5 per

cent. ? 11. What is the interest of $ 35.61 from November 11, 1861, to December 15, 1863 ?

Ans. $ 4.474. 12. What is the interest of $ 16.76 from December 17, 1841, to January 17, 1852 ?

Ans. $ 10.139+ 13. What is the interest of $ 1728.19 from May 7, 1854, to July 17, 1860, at 4 per cent. ?

Ans. $ 26.762. 14. What is the interest of $ 397.16 for 1 year 6 months and 1 day, at 54 per cent. ?

Ans. $ 32.826. 15. What is the amount of $ 100.25 for 2 months and 29 days, at 4 per cent.?

Ans. $ 101.241. 16. What is the interest of $ 51.17 for 9 months and 29 days, at 4 per cent.?

Ans. $ 1.699. 17. What is the interest of $ 42.20 for 1 year and 16 days, at 41 per cent. ?

18. What is the interest of $ 16.25 for 2 years, at 3 pet cent. ?

Ans. $ 0.975. 19. What is the interest of $ 96.84 from November 27, 1849, to July 3, 1852, at 7} per cent. ? Ans. $ 18.883.

20. What is the interest of $ 786.97 from October 19, 1857, to August 17, 1861, at 74 per cent. ?

21. What is the interest of $ 71.091 from July 29, 1853, to June 19, 1857, at 12 per cent. ?

Ans. $33.175. 22. What is the amount of $ 369.29 for 2 years 3 months and 1 day, at 9 per cent. ?

Ans. $ 444.163. 23. What is the interest of $ 76.35 for 1 year 8 months and 18 days ?

Ans. $ 7.864. 24. What is the interest of $ 47.15 for 1 month and 19 days, at 131 per cent. ?

Ans. $ 0.886. 25. What is the interest of $ 36.72 from May 16, 1829, to February 18, 1857, at 7 per cent. ?

Ans. $ 71.342. 26. What is the interest of $ 35.50 for 3 years 5 months and 20 days, at 7 per cent. ?

Ans. $ 8.628. 27. What is the amount of $ 496.30 for 6 months and 20 days, at 7 per cent. ?

Ans. $ 515.60. 28. What is the interest of $ 691.04 for 1 month 3 days, at 5 per cent. ?

Ans. $ 3.167. 29. What is the interest of $ 9750 for 4 months, at 2 per cent. a month ?

Ans. $ 780. 30. What is the interest of $ 9162 for 3 months, at 11 per cent. a month ?

Ans. $ 412.29. 31. What is the interest of $ 1500 for 7 months 20 days, at 10 per cent. ?

Ans. $ 95.833. 32. What is the interest of $ 640.50 for 10 months and 26 days, at 10

per
cent. ?

Ans. $ 58.00. 33. What is the interest of $ 3178 for 15 months and 15 days?

34. If a banker borrow $ 10,000 in Boston at 6 per cent., and let the same in Wisconsin at 7 per cent., how much does • he make by the operation in that way in 2 years and 63 months ?

Ans. $ 255.555. 356. To reckon interest for any number of days, when 12 months of only 30 days each, or 360 days, are considered a year.

FIRST OPERATION.

.015 1

Ex. 1. What is the interest of $ 460 for 93 days ?

Ans. $ 7.13.

We multiply the principal Principal,

$ 4 6 0 by of the number of days, of 93d. = 15ļd. ;

considered as thousandths;

since the interest of $ 1 at 6 2 3 0 0

per cent. for 6 days is 1 mill 4 60

or 1 thousandth of a dollar,

2 30 (Art. 352,) and for any Interest,

$ 7.1 30 Ans. other number of days, at

the same per cent., must be one sixth as many mills or thousandths of a dollar as there are days

SECOND OPERATION.

Principal,

$ 4 60 Ito of the principal,

4.60 Interest for 60d. } of the interest for 60d. 2.30 Interest for 30d. to of the interest for 30d. .2 3 Interest for 3d.

Ans. $ 7.1 3 Interest for 93d. 93 days 60 days + 30 days + 3 days. Now, since the interest of any sum at 6 per cent. for 2 months, or 60 days, equals ido of the principal (Art. 352), ito of $ 460 :$ 4.60 will be the interest for 60 days; 1 of the interest for 60 days, or $ 2.30, will be that for 30 days; and io of the interest for 30 days, or $ 0.23, will be that for 3 days. The interest for the several parts of the time added together must give the interest for the whole time, or 93 days.

RULE. Multiply the principal by the number denoting one sixth of the number of days expressed decimally as thousandlths. Or,

Divide the principal by 100, and take such a part or parts of the quotient as the given number of days is of 60 days. The result will be the interest at 6 per cent., from which it may

be found for any other rate, as in Art. 355.

NOTE 1. – One sixth of the number of days in any number of months of 30 days each is equal to 5 times the number of months. Thus, one sixth of the number of days in 7 months equals 7 X 5, or 35 days; and one sixth of the number of days in 9 months and 13 days equals (9 X 5) + (13 ; 6), or 45 + 21 = 471 days.

NOTE 2. - It is a common practice among mercantile men, in calculating interest, to consider a year to consist of only 360 days, but the laws of some of the States require 365 days to a year. 366 days are in fact only 369 = 7% of a common year, and therefore are 7 less than what perfect accuracy would require. Hence, when the year is considered to be one of 365 days, the interest as found by the rule must be diminished by ts of itself ; Or, we may multiply the principal by the number of days, and, if the rate be 6 PER CENT., diride by 6083}; if the rate be 7 PER CENT., divide by 5214. and if the rate be 5 PER CENT., divide by 7300.

EXAMPLES.

2. What is the interest of $ 96 for 33 days, at 7 per cent. ?

Ans. $.616. 3. What is the interest of $ 320.40 for 63 days, at 5 per cent. ?

Ans. $ 2.803. 4. What is the interest of $ 131.20 for 123 days?

Ans. $ 2.689. 5. What is the interest of $ 26.60 for 78 days?

6. What is the interest of $ 5780 for 153 days, at 10 per cent. ?

Ans. $ 245.65. 7. What is the interest of $ 105.10 for 48 days, at 12 per cent. ?

Ans. $ 1.681. 8. What is the interest of $ 13.62 for 93 days, at 74 per cent. ?

9. What is the interest of $ 4580 for 253 days, at 53 per cent.?

Ans. $ 177.02913. 10. What is the interest of $ 3140 for 273 days, at 7 per cent. ?

Ans. $ 166.6813. 11. What is the interest of $ 10550 for 243 days, at 8 per cent. ?

Ans. $ 569.70. 12. What is the arount of $ 33.44 for 333 days ?

Ans. $ 35.295. 13. What is the amount of $ 71.60 for 3 months and 18 days?

14. What is the interest of $ 92.96 for 4 months and 3 days, at 7 per cent. ?

Ans. $ 2.223. 15. What is the interest of $ 144.50 for 144 days, allowing 365 days to the year, at 5 per

cent.?

Ans. $ 2.85. 16. What is the interest of $ 761.81 for 165 days, allowing 365 days to the year?

Ans. $ 20.662. 17. What is the interest of $ 560 for 183 days, allowing 365 days to a year, at 7 per cent. ?

Ans. $ 19.65. 18. What is the interest of $ 1960 for 93 days?

19. What is the amount of $ 1000 for 1 month and 3 days?

Ans. $ 1005.50. 20. What is the amount of $ 7300 for 18 days, at 6 per cent. ?

Ans. $ 7321.90.

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