Introduction to The National Arithmetic, on the Inductive System: Combining ...
Από τον/την Benjamin Greenleaf
4. What is the value of .965625 of a mile ?
Ans. 7fur. 29rd. 5. What is the value of .94375 of an acre ?
Ans. 3R. 31p. 6. What is the value of .815625 of a pound Troy?
Ans. Soz. 15dwt. 18gr. 17. What is the value of .5555 of a pound apothecary's weight?
Ans. 6%. 53.00. 1915gr.
EXERCISES IN DECIMALS.
per ton ?
acre ?
1. What is the value of 15cwt. 3qr. 141b. of coffee at . $9.50 per cwt. ?
Ans. $ 150.81+ 2. What cost 17T. 18cwt. lqr. 71b. of potash at $53.80
Ans. $ 963.86+. 3. What cost 37A. 3R. 16p. of land at $ 75.16 per
Ans. $2844.80+. 4. What cost 15yd. 3qr. 2na. of cloth at $ 3.75 per yard?
Ans. $ 59.53+. 5. What cost 15% cords of wood at $ 4.62} per cord ?
Ans. $ 71.10+ 6. What cost the construction of 17m. 6fur. 36rd. of railroad at $ 3765.60
mile ? Ans. $ 67263.03+. 7. What cost 27hhd. 21gal. of temperance wine at: $ 15.371 per hogshead ?
Ans. $ 420.24+. 8. What are the contents of a pile of wood, 18ft. 9in. long, 4ft. 6in. wide, and 7ft. 3in. high ?
Ans. 611ft. 1242in. 9. What are the contents of a board 12ft. 6in. long, and 2ft. Sin wide ?
Ans. 34ft. 54in. 10. Bought a cask of vinegar containing 25gal. 3qt. lpt. at $0.37} per gallon ; what was the amount ?
Ans. $ 9.70+. 11. Bought a farm containing 144A. BR. 30p. at $97.62; per acre ; what was the cost of the farm ?
Ans. $ 14149.52+.
12. Sold Joseph Punson 3T. 18cwt. 21lb. of salt hay, at $9.371 per ton. He having paid me $ 20.25, what remains due ?
Ans. $ 16.40+. 13. If 7 of a cord of wood cost $5.50, what cost one cord ? What cost 7 cords ? Ans. $ 48.71+.
I Section 33.
SIMPLE INTEREST.
INTEREST is the compensation, which the borrower of money makes to the lender.
PRINCIPAL is the sum lent.
Amount is the interest added to the principal.
Per Cent., a contraction of per centum, is the rate established by law, or that which is agreed on by the parties, and is so much for a hundred dollars for one year.
GENERAL RULE.
Let the per cent. be considered as a decimal of a hundred dollars, and multiply the principal by it, and the product is the interest for one year ; but, if it be required to find the interest for more than one year, multiply the product by the number of years.
NOTE. The decimal for 6 per cent. is .06; for 7 per cent. .07; for 8 per cent. .08; for 94 per cent. .0925; for 25 per cent. .025, &c. The decimals must be pointed off as in Multiplication of Decimal Fractions.
This rule is obvious from the fact, that the rate per cent. is such a part of every hundred dollars. Thus, 6 per cent. is Too of the principal.
NOTE. When no particular per cent. is named, 6 per cent. is to be understood, as it is the legal interest in the New England States generally. In New York the legal interest is 7 per cent.
1. What is the interest of $ 346 for one year ?
Ans. $ 20.76. 346
There being two places of deci.06
mals in the multiplier, we point off
two in the product. $20.76 2. What is the interest of $ 67.87 for 5 years ?
Ans. $ 20.36. OPERATION. 67.87 .06
There being two places of deci
mals in the multiplicand, and two in 4.0 722
the multiplier, we point off four 5
places in the product. $20.3610 3. What is the interest of $ 197 for 1 year ?
Ans. $ 11.82. 4. What is the interest of $ 1728 for 3 years?
Ans. $ 311.04. 5. What is the interest of $ 69 for 2 years ?
Ans. $8.28. 6. What is the interest of $ 1775 for 7 years ?
Ans. $ 745.50. 7. What is the interest of $ 987 for 10 years ?
Ans. $ 592.20. 8. Required the interest of $69.17 for 4 years.
Ans. $ 16.60. 9. Required the interest of $ 96.87 for 11 years.
Ans. $ 63.93. 10. Required the interest of $ 1.95 for 18 years.
Ans. $ 2.10. 11. Required the interest of $ 1789 for 20 years.
Ans. $ 2146.80. 12. Required the interest of $ 666.66 for 30 years.
Ans. $ 1199.98. 13. What is the amount of $ 98,50 for 5 years ?
Ans. $ 128.05. 14. What is the amount of $ 168.13 for 11 years ?
Ans. $ 279.09. 15. What is the amount of $ 75.75 for 17 years?'
Ans. $ 153.01. 16. Required the amount of $ 675.50 for 100 years.
Ans. $ 4723.50.
II. To find the interest for months, at six per cent.
RULE.
Multiply the principal by half the number of months, expressed decimally as a per cent. ; that is, for 12 months multiply by .06 ; for 8 months multiply by .04; for 7 months .035; for 1 month .005, and point for decimals as in the last rule.
Note. It is obvious, that if half the number of months were 12, it would be 1 per cent. a month, that is, half the months will be the per cent. Q. e. d.
1. What is the interest of $ 486 for 10 months ?
48 6 principal.
.0 5 months decimal of the per cent.
$2 4.30 Ans. 2. What is the interest of $ 1728 for 18 months ?
Ans. $ 155.52. 3. What is the interest of $ 16.87 for 20 months ?
Ans. $ 1.68. 4. Required the interest of $ 118.15 for 30 months.
Ans. $ 17.72. 5. Required the interest of $97.16 for 17 months.
Ans. $ 90.83. 7. Required the amount of $978.18 for 27 months.
Ans. $ 1110.23. 8. Required the amount of $ 87.96 for 1 month.
Ans. $ 88.39. 9. Required the amount of $ 81.81 for 100 months.
Ans. $ 122.71. 10. Required the amount of $ 0.87 for 87 months.
Ans. $ 1.24. III. To find the interest for any sum for months and days, at 6 per cent.
To one half of the months expressed decimally as in the last rule, annex one sixth of the days. With this multiply
the principal, and point off in the product as many deci. mals as there are in both factors ; the first two figures at the right of the separatrix are cents, and the third is mills.
Note. If any other per cent. is required, proceed as before, and then divide the product by 6, and multiply the quotient by the rate required. The same result will be obtained if we multiply by the required rate, and divide the product by 6. 1. What is the interest of $ 57.50 for 10 months and 24 days?
Ans. $ 3.105.
OPBRATION.
We multiply by .054, because .05 .054
is the rate per cent. for 10 months ; 23000
and we annex the 4, because 4 is } 28750 of the 24 days.
3.1 050 0 2. What is the interest of $178.75 for 17 months 17 days at 7 per cent. ?
Ans. $ 18.31.
.0876 1 251 25 143 000
14895 6)1570020 261670
18.3 1690 3. What is the interest of $ 761.75 for 14 months and 18 days?
Ans. $ 55.60. 4. What is the interest of $1728.19 for 17 months and 10 days?
Ans. $ 149.77. 5. What is the interest of $88.96 for 16 months 6 days ?
Ans. $ 7.20. 6. What is the interest of $ 107.50 for 1 month 29 days?
Ans. $ 1.05. 17. What is the interest of $ 87.25 for 20 months 5 days ?
Ans. $ 8.79. 8. What is the interest of $ 73.16 for 19 months 23 days?
Ans. $ 7.3.