7. What is the amount of $60, at 83 per cent., for 3 years and 3 months? 8. What is the amount of $64, at 12} per cent., for 2 years and 9 months? 9. What is the amount of $36, at 163 per cent., for 2 years and 3 months? 10. What is the amount of $84, at 25 per cent., 2 years and 6 months? for 11. At what rate per cent. will $6 gain 45 cents interest in 1 years? per cent., Solution. The interest of $6 for 1 year, at 1 is 6 cents, and for 14 years it is 1 times 6 cents, or 9 cents. If $6, at 1 per cent., gains 9 cents, then to gain 45 cents will require as many per cent. as 9 cents is contained times in 45 cents: 9 cents in 45 cents, 5 times; therefore, $6, at 5 per cent., will gain 45 cents in 1 years. Or, thus: Since the interest for 14 years or years is 45 cents, for year it is of 45 cents, or 15 cents, and for years or a whole year it is 2 times 15 cents, or 30 cents; 30 cents is 130 of $6; 150 is 5 per cent.; therefore, $6, at 5 per cent., gains 45 cents in 1 years. = 12. At what rate per cent. will $8 gain 96 ce ts in 1 year and 6 months; that is, in 13 years? 13. At what per cent. will $100 gain $10 in 13 years? 14. At what per cent. will $50 gain $10 in 2 years? 15. At what per cent. will $12 gain 80 cents in 1 year and 4 months? 16. At what per cent. will a given principal double itself in 20 years? Solution. Any principal will double itself in 1 year, at 100 per cent. ; and, therefore, in 20 years, at 100 per cent., viz., 5 per cent. of 17. At what per cent. will any principal double itself in 25 years? In 10 years? 12 years? 50 years? 16 year? 33 years? 5 years? 4 years? 18. In what time will $6, on interest at 5 per cent., gain 70 cents? Solution. $6, at 5 per cent., gains 30 cents in 1 year; 30 cents in 70 cents, 24 times; therefore, $6, at 5 per cent., will gain 70 cents in 2 years, or 2 years and 4 months. 19. In what time, at 6 per cent., will $10 gain $3? 20. In what time, at 10 per cent., will $100 gain $25? 21. In what time, at 4 per cent., will $4 gain 24 cents? 22. In what time, at 8 per cent., will $50 gain $23? 23. In what time, at 5 per cent., will a given principal double itself? Solution. Any principal, at 1 per cent., will double itself, i. e. it will gain 100 per cent., in 100 years; and at 5 per cent., in of 100 years, viz., 20 years. 24. In what time, at 4 per cent., will any principal double itself? In what time, at 6 per cent.? At 8 per cent.? At 20 per cent.? At 25 per cent.? At 2 per cent.? At 50 per cent.? At 12 per cent.? At 64 per cent.? At 163 per cent.? At 33 per cent.? LESSON IV. 1. WHAT principal, at 6 per cent., will gain 36 cents in 1 year and 6 months? Solution. $1, at 6 per cent., gains 9 cents in 1 year and 6 months; 9 cents in 36 cents, 4 times; therefore, $4, at 6 per cent., will gain 36 cents in 1 year and 6 months. Or, since the interest of any sum for 1 year and 6 months, at 6 per cent., is T8 of the principal, it follows that 36 cents is 8 of the required principal; hence, of 36 cents, or 4 cents, is To, and 188 is 100 times 4 cents, which is 400 cents, or $4; therefore, etc. 2. What principal, at 5 per cent., will gain 60 cents in 2 years? 3. What principal, at 8 per cent., will gain $2 in 6 months? 4. What principal, at 10 per cent., will gain $15 in 1 year? 5. What principal, at 8 per cent., will gain $60 in 3 years and 9 months? 6. What principal, at 10 per cent., will amount to $6.60 in 1 year? Solution. The amount of $1 for 1 year, at 10 per cent., is $1.10; $1.10 in $6.60, 6 times; therefore, $6, at 10 per cent., will amount to $6.60 in 1 year. Or, the interest of any sum for 1 year, at 10 per cent., is of the principal, and this added to the principal, 18, makes the amount of the principal; hence, $6.60 is 1 of the principal, and of $6.60, or 60 cents, is, and 18, or the whole principal, is 10 times 60 cents = 600 cents, or $6; therefore, etc. 7. What principal, at 5 per cent., will amount to $22 in 2 years? To $44 in 2 years? 8. What principal, at 8 per cent., will amount to $58 in 2 years? To $84 in 11⁄2 years? 9. What principal, at 4 per cent., will amount to $66 in 5 years? To $280 in 10 years? 10. What principal, at 12 per cent., will amount to $250 in 2 years? To $121 in 3 years? 11. What principal, at 163 per cent., will amount to $42 in 1 year? To $80 in 2 years? 12. What principal, at 6 per cent., will amount to $10.60 in 1 year? To $21.80 in 1 year and 6 months? 13. What sum can I obtain at a bank for a note of $80, payable in 60 days? Solution. The interest of $80 for 60 days is 80 cents, which, taken from $80, leaves $79.20; therefore, etc. 14. What sum can I obtain at a bank for a note of $48, payable in 45 days? What sum for a note of $64, payable in 75 days? SECTION NINTH. LESSON I. 1. BOUGHT 2 lb. of figs, at 20 cents per pound, and gave in payment a quarter of a dollar, a dime, and the rest in cents; how many cents did I give? 2. I have a rectangular field 20 rods long and 15 rods wide; what will it cost to build a wall around it, at $1.50 a rod? 3. I have a field containing 3 roods and 10 rods; what is it worth, at $2 per square rod? 4. What is the cost of a load of wood which measures 1 cord and 2 cord feet, at 75 cents per cord foot? 5. How many days from July 4th, at 9 o'clock in the morning, to Aug. 10th, at 9 o'clock in the evening? 6. What cost 3 score bushels of corn, at 2 of a dollar a bushel? 7. If a ship sail 180 miles each day, how far does she sail in a week? 8. Bought a load of wood which measured 9 cord feet; of the load was pine, at $4 a cord, and the rest was oak, at 75 cents a cord foot; what was the cost of the load? 9. What cost 10 acres of land, at $20 per acre? 10. I have a square piece of land each side of which is 33 feet long; how many rods is it round this piece? 11. If it takes 16 yards of silk to make a dress, what will the silk for 2 dresses cost, at 14 dollars per yard? 12. I have a rectangular garden which is 12 rods long and 7 rods wide; how many square rods does it contain? 13. Mr. Smith has a rectangular garden, 6 rods wide, and containing 48 square rods; how long is it? 14. Mr. French has a rectangular garden 10 rods leng and containing 70 square rods; how wide is it? 15. A man bought a share of the Boston and Maine Railroad stock for $100, and sold it for $103; what per cent. on the purchase money did he gain? 16. A grocer bought a box of sugar for $12, and sold it so as to gain 5 per cent.; how much did he gain? 17. A merchant bought a piece of silk for $75, and sold it so as to gain 10 per cent.; how much did he gain? What did he receive for the silk? 18. A shoedealer bought boots at $4 a pair, and sold them at $5; what per cent. did he gain? He bought others at $5, and sold them at $4; what per cent. did he lose? 19. A grocer bought molasses at 40c. per gallon; how shall he sell it to gain 25 pcr cent.? 20. A merchant bought goods for $50, but, they being damaged, he is willing to lose 20 per cent.; for what sum is he willing to sell them? 21. A laborer agreed to work 5 months for 60 dol lars; how much did he receive for a month? How much for a week, allowing 4 weeks to the month? How many shillings a day, allowing 6 working-days to the week? 22. If a melon is worth 8 are 44 oranges worth? oranges, how many melons 23. A man sold 24 hens a: the rate of 3 for a dollar; how many dollars did he receive? 24. If wine is worth 24 cents a pint, what is 1 gi worth? What are 3 gills worth? 25. At 80 cents a bushel, what is a peck of corn worth? What is a half peck worth? 26. Five boys bought a sled for 90 cents, and sold it for 75 cents; sharing the loss equally, what did each boy lose by the bargains? 27. A man paid $35 for wood, at $7 a cord; how many cords did he buy? |
