93. 1. In what time, at 5 per cent., will $60 gain $15 interest?

ANALYSIS. The gain, or interest, is, or of the principal, equal to 25 per cent. of the principal. (77, Ex. 7.) If a given principal gain 5 per cent. in 1 year, it will require as many years to gain 25 per cent. as 5 per cent. is contained times in 25 per cent., or 5 years. Therefore, &c.

Or thus: Since $60 in 1 year, at 5 per cent., will gain $3 interest, it will require as many years for $60 to gain $15 interest, as $3 is contained times in $15, which is 5 times.

2. How long will it take $120 to gain $24 interest, at 6 per cent.?

3. In what time will $500 gain $35, at 7 per cent.?

4. In what time will $120 gain $40, at 10 per cent.?

5. In what time will $80 gain $6, at 3 per cent.? 6. In what time will $300 gain $84, at 7 per cent.?

7. In what time will $160 gain $20, at 64 per

cent.?

8. In what time will $49 gain $12.25, at 5 per cent.?

9. In what time will any given principal double itself at 4 per cent.?

ANALYSIS. Since, to double itself, any sum of money must gain 100 per cent., at 1 per cent., it will require 100 years, at 4 per cent., 1 of 100 years, or 25 years. Therefore, &c.

10. In what time will a given principal double itself at 5 per cent. ?

11. In what time will a given principal double it

self at 7 per cent.?

12. In what time will a given principal double itself at 6 per cent.?

13. In what time will a given principal double itself at 10 per cent. ?

14. In what time will $500 double itself, at 12 per cent.?

15. In what time will $175 double itself at 20 per cent.?

16. In what time will a given principal treble itself at 5 per cent.?

ANALYSIS. A given principal will treble itself at 1 per cent. in 200 years; at 5 per cent. in of 200 years, or 40.. years.

17. In what time will $100 treble itself at 6 per cent.? at 7 per cent.? at 8 per cent.? at 10 per cent.?

94. 1. A man loaned $75 for 4 years, and received $18 interest; what was the rate per cent.?

ANALYSIS. Since the gain, or interest, for 4 years, is , or 25 of the principal, for 1 year it is + of 25, or του of the principal, equal to 6 per cent. Therefore, &c.

Or, thus: At 1 per cent., the interest of $1 for 4 years is 4 cents, and of $75 it is 75 times 4 cents, which are 300 cents, equal to $3. Since $3 interest is 1 per cent. of $75 for 4 years, $18 interest is as many per cent. as $3 is contained times in $18, which is 6 times, equal to 6 per

cent.

2. At what per cent. will $200 gain $49 interest in 3 years?

3. At what per cent. will $60 gain $25 interest -in 4 years?

4. At what per cent. will $90 gain $27 in 6 years?

5. At what per cent. will $12 gain $5 in 16

years ?

At what per cent. will $400 gain $55 interest

6. in 21 years?

7.

At what per cent. will $150 gain $44 interest

in 33 years?

8. At what per cent. will $125 gain $37.50 interest

in 5 years?

9. At what per cent. will $800 gain $75 interest in 1 year and 3 months?

10. At what per cent. will $180 gain $45 interest in 3 years and 9 months?

11. At what per cent. will $1250 gain $312.50 interest in 2 years 6 months ?

12. At what per cent. will $2500 gain $200 interest in 1 year and 4 months?

13. At what per cent. will a given principal double itself in 5 years ?

ANALYSIS. Since a given principal must gain 100 per cent. to double itself in 1 year, to double itself in 5 years will require of 100 per cent., or 20 per cent. Therefore, &c.

14. At what per cent. will a given principal double itself in 10 years?

15. At what per cent. will a given principal double itself in 12 years 6 months?

16. At what per cent. will $200 double itself in 4 years?

17. At what per cent. will $100 double itself in 8 years?

18. At what per cent. will $150 double itself in 15 years?

19. At what per cent. will $500 double itself in 16 years 8 months?

20. At what per cent. will $175 double itself in 2 years 6 months?

95. The present worth of a note payable at a future time is such a sum as, put at interest at the given rate per cent. until it becomes due, will amount to the face of the

note.

Discount is an allowance made for the payment of money before it becomes due, and is obtained by subtracting the present worth from the given sum or face of the note.

1. What is the present worth of $180 payable in 3 years 4 months at 6 per cent.?

ANALYSIS. Since the interest for 3 years 4 months at 6 per cent. is of the principal, (88,) the amount, $180, is equal to the principal, &, added to the interest, t, equal to

of the principal. Since $180 is of the principal, & of $180, or $30, ist, and $30 is of 5 times $30, or $150. Therefore, &c.

NOTE. The discount is the difference between $180 and $150, which is $30.

2. What is the present worth of a note for $36.90, payable in 2 years 6 months, at 5 per cent.?

3. What is the present value of a note for $54, due in 5 years, and bearing interest at 7 per cent.? 4. What is the present value of a debt of $124.40, due in 4 years 2 months, at 8 per cent. interest ?

5. What is the discount of $2100, due in 1 year 3 months, at 4 per cent.?

6. What is the discount on a note of $560, payable in 2 years, at 6 per cent. interest?

7. What is the difference between the interest and the discount of $130, due 10 months hence, at 10 per cent. ?

8. A man, having a span of horses for sale, offered them for $480 cash in hand, or a note of $550 due in 1 year 8 months without interest. The buyer accepted the latter offer; did the seller gain or lose by his offer, and how much, allowing the money to be worth 6 per cent.?

96. 1. B sold a horse for of 18 times the cost; what was the gain per cent.?

2. A cow purchased for $28 in the spring was sold for $21 in autumn; what was the loss per cent.?

3. An old lady bought 30 apples of John at the rate of 2 for a cent, as many more of William at the rate of 3 for a cent, and sold the whole at the rate of 5 for 2 cents; did she gain or lose, and at what rate per cent. ?

4. Did she gain or lose on the purchase made of John or William, and at what rate per cent. on the amount of the purchase?

5. A hogshead of molasses was bought for $20; 114 per cent. of it leaked out; how must the remainder be sold per gallon to gain 40 per cent. on the cost?

6. A manufacturer sold 2 machines for $391 each; on one he gained 15 per cent., on the other he lost 15 per cent.; did he gain or lose on the sale of both, and how much?

7. How much wheat must be taken to mill, that 6 bushels may be retained after giving toll of 6 pounds per bushel, or 10 per cent. for grinding ?

8. A man brought home 1500 feet of lumber after giving 37 per cent. of the whole for sawing; how much lumber did he have sawed?

9. A farmer sold 2 horses for $150 apiece; on one he gained 25 per cent., on the other he lost 25 per cent.; did he gain or lose on both, and how much?

10. For hulling barley, 36 per cent. is taken for pay; at this rate, how many bushels must be taken that 32 bushels be returned after hulling?

11. In a school district $57 was to be collected for teacher's wages; the collector was to have 5 per cent. on all moneys collected; how much must he collect to pay his fee and the teacher?