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7. What principal will, in 43 years, at 6 per cent.,
amount to $640?

8. What principal will, in 54 years, at 7 per cent.,
amount to $42 ?

9. What principal will, in 64 years, at 7 per cent.,
amount to $87?

10. What principal will, in 8 years, at 6 per cent.,
amount to $76!

REMARK.-The present worth of a debt payable at some future
time, without interest, is such a sum, as will, in the given time,
and at the given rate per cent., amount to the debt. Hence, the
present worth of any sum of money, payable at some future time
without interest, may be found in the same way that we found
the principal, when we had given the amount, time, and rate
per cent.

See the above solution.

11. What is the present worth of $26, due 5 years
hence, at 6 per cent.?
Ans. $20.
12. What is the present worth of $14, due 8 years
hence, at 5 per cent.?

13. What is the present worth of $110, due 5 years
hence, at 5 per cent.?

14. What is the present worth of $86, due 8 years
hence, at 9 per cent.?

15. What is the present worth of $102, due 9 years
hence, at 4 per cent.?

16. What is the present worth of $72, due 4 years
hence, at 5 per cent.?

17. What is the discount on $46, due 3 years hence,
at 5 per cent. ?

REMARK.-The discount equals the amount minus the present

worth.

18. What is the discount on $54, due 5 years hence,
at 7 per cent. ?

19. What is the discount on $65, due 5 years hence,
at 6 per cent.?

20. What is the discount on $93, due 3 years hence,
at 8 per cent.?

21. What is the present worth of $186, due 4 years hence, at 5 per cent.?

22. What is the present worth of $66, due 5 years hence, at 6 per cent.?

23. What is the present worth of $128, due 43 years hence, at 6 per cent.?

LESSON XVI.

1. If I sell cloth, at $2.50 a yard, and thereby gain 25 per cent.; what did it cost a yard?

SOLUTION.-If I gain 25 per cent. I gain of the cost; to which add, the cost, and I have of the cost equal to $2.50. If of what I gave for it, is $2.50, of the cost is of $2.50, or 50 cents; and (the cost) is 4 times 50 cents, which are 200 cents, or $2.

2. A horse was sold for $38, which was at a loss of 5 per cent. What did the horse cost?

3. If I sell cloth, at $2.50 a yard, and thereby gain 25 per cent., how must I sell it a yard, to lose 20 per cent.?

4. If I sell cloth, at $4.40 a yard, and thereby gain 10 per cent., how ought I to sell it, to lose 25 per cent.

5. If by selling a piece of cloth for $46, I gain 15 per cent., how ought I to have sold it, to have lost 30 per cent.?

6. A sold his horse for $105, and thereby gained 5 per cent. on the cost; for what ought he to have sold it, to have lost 10 per cent.?

7. A farm was sold for $495, which was 10 per cent. less than what it was worth; for what ought it to have been sold, to have received 40 per cent. more than its value?

8. A mechanic lost 20 per cent. on the cost of a wagon, by selling it for $40; for what ought it to have been sold, to have gained 30 per cent. ?

9. A horse was sold for $90, which was 10 per cent. less than its value; what would have been the gain per cent., if it had been sold for $120?

10. A farm was sold for $690, which was 8 per cent. less than its value; what would have been the gain per cent., if it had been sold for $850?

11. A book was sold for 90 cents, which was 10 per cent. less than its value; what would have been the gain per cent., if it had been sold for $1.50?

12. A man sold two watches, at $12 each; on one he gained 50 per cent., and on the other he lost 50 per cent. Did he gain or lose by the bargain, and how much?

13. An individual sold two gold pencils, at $6 apiece; on one he gained 20 per cent., and on the other he lost 20 per cent. Did he gain or lose, and how much?

14. A farmer sold two horses at $210 apiece; for one he received 25 per cent. more than its value, and for the other 25 per cent. less than its value. Did he gain or lose by the bargain, and how much?

15. A merchant sold a quantity of cloth for $280, and by so doing lost 60 per cent.; he then sold another quantity for $80, and thereby gained 60 per cent. Did he gain or lose by the operation and how much?

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LESSON XVII.

1. An individual was ordered to collect $190, and his own fee, which is to be 5 per cent, on all the money collected. How much should he receive?

SOLUTION. He is to receive 5 per cent., or or of all he collects. 20, all he collects, minus, his fee, equals of all he collects, or $190, the amount he is to pay his employer. If 8 of what he collects equals $190, is of $190, which

is $10; and 3% (what he collects) is 20 times $10, or $200. Therefore he must receive $200-$190 $10.

2. How much ought A to receive for collecting $90 and his own fee, of 10 per cent. on all he collects?

3. What amount of money will be sufficient to pay a debt of $38 and the collector's fee, which is 5 per cent. on all the money collected?

4. How much cider must that man make to bring away 15 barrels, after the owner of the mill receives 16 per cent. of all he has made?

he

5. How much grain must a farmer take to mill, that may bring away the flour of 1 bushel, after the miller has taken 10 per cent. of all he took there?

MISCELLANEOUS QUESTIONS.

1. At 5 per cent. for 4 years, what part of the prineipal equals the interest?

2. In how many years, at 4 per cent., will a given principal amount to the same, as it would in 8 years, at 6 per cent.?

3. At what per cent. will a given principal, in 14 years, amount to the same, as it would in 12 years at 7 per cent.?

4. If

of the principal equals the interest, what is the rate per cent.?

5. The rent of B's farm, for 8 years amounted to of its value. What per cent. did he annually receive on the value of his farm?

6. What is the interest of $75, for 5 years, at 6 per cent.?

7. What principal will, in 7 years, at 8 per cent., give $24 interest?

8. What principal will, in 44 years, at 5 per cent,, amount to $155?

9. At what per cent., will a given principal double itself, in 12 years?

10. The interest of A's and B's fortune, for 8 years, at 5 per cent., is $420. What is the fortune of each, provided A's fortune is twice B's?

What is each of

11. The interest of of A's and of B's fortune, for 7 years at 5 per cent., is $2100. their fortunes, provided

B's?

of A's fortune equals

of

12. B sold his horse, for of 14 times what it cost; what did he lose per cent.?

13. What is the interest of $540 for 4 years, at 5 per cent.?

14. What is the interest of $180, for 5 years and 9 months, at 63 per cent.?

15. What principal will in 4 years 7 months and 6 days, at 61 per cent., amount to $412!

16. The interest of the cost of B's horse, sleigh and wagon, for 6 years, at 5 per cent., is $69. What is the cost of each, provided their prices are to each other respectively, as, and ??

17. What principal will, in 8 years and 8 months, at 7 per cent., amount to $419?

18. What principal will, in 5 years 9 months and 18 days at 10 per cent., give $116 interest?

19. In what time, will $420, at 5 per cent., give $147 interest?

20. If the interest of $200, for 1 year and 6 months, is $18, what is the rate per cent.?

21. At what per cent., will $500, in 4 years and 9 months, give $190 interest?

22. At what per cent., will $500, in 22 years and 6 days, amount to $1821?

23. At what per cent. will a given principal double itself, in 20 years?

24. In what time will a given principal double itself, at 12 per cent. ?

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