16. If the interest of $300 for 2 years is $48, what is the rate per cent.?

NOTE. Since the interest of $300 for 2 years, at 1 per cent., is $6, $48 will be as many per cent. as $48 contains times $6.

17. If the interest of $200 for 2 years is $12, what is the rate per cent.?

18. If the interest of $400 for 3 years is $24, what is the rate per cent.?

19. If the interest of $150 for 3 years and 4 months is $35, what is the rate per cent.?

20. If the interest of $25 for 1 year and 8 months is $1, what is the rate per cent.?

NOTE. The interest of $25 for 1 year and 8 months, at 1 per cent., is 13 times Too of $25=5 of $25-$1, and the rate per cent. required will be as many per cent. as $11⁄2 is contained times in $1, which are 1223 times. Therefore, 2 per cent. is the answer.

21. If the interest of $50 for 1 year and 3 months is $3, what is the rate per cent.?

22. If the interest of $75 for 4 years and 2 months is $12, what is the rate per cent.?

23. A man paid $8 for the use of $48 for 1 year and 4 months; what was the rate per cent. ?

24. John Niles lends Harry Hubbard $30 for 2 years and 6 months; Harry has to pay at the end of the time $36; what is the rate per cent.?

NOTE.The principal, $30, has to be paid back, and is of course a part of the $36; the remainder, $6, is the interest, by which the rate per cent. is to be found.

25. A note of $100, being on interest 2 years and 2 months, amounted to $125; what was the rate per cent.?

26. A gentleman lent $60 for 1 year and 6 months, and received $90; what was the rate per cent.?

LESSON XLVII.

1. What principal, at 10 per cent., is sufficient to gain $6 in 4 years?

NOTE. Since the interest of $1 for 4 years, at 10 per cent., is 40 cents, $6 is the interest of as many dollars as 40 cents or 4 dimes is contained times in $6 or 60 dimes, which are 15; therefore, $15 is the answer.

2. What principal, at 4 per cent., is sufficient in 2 years to gain $8?

3. What is the principal that, in 4 years, at 3 per cent., will gain $6?

4. What principal, at 6 per cent., is sufficient in 5 years to gain $10?

5. What principal is sufficient in 2 years and 4 months, at 4 per cent., to gain $64?

6. What principal is sufficient in 2 years, at 8 per cent., to gain $10?

7. What principal is sufficient in 6 years, at 1 per cent., to gain $20?

8. What principal, at 4 per cent., in 1 year and 7 months, will gain $5?

9. What principal, in 6 years and 4 months, at 6 per cent., will gain $18?

10. What principal is sufficient in 7 years to gain $18, at 7 per cent.?

11. The interest on a note for 4 years and 2 months, at 4 per cent., was $60; what was the principal?

12. If the interest of $50, at 6 per cent., is $6, how long was it on interest?

NOTE. Since $50 at 6 per cent. will require 1 year to gain $3, it will require as many years to gain $6 as $3 is contained times in $6, which are 2 times. Therefore, 2 years is the an

swer.

13. If the interest of $60, at 2 per cent., is $12, how long has it been on interest?

14. How long must $100 be on interest, at 4 per cent., to gain $40?

15. A note of $80, being on interest at 8 per cent., amounted to $160; how long was it on interest?

16. How long must $10 be on interest, at 5 per cent., to gain $3?

17. If the interest of $20, at 4 per cent., is $4, how long a time has it been on interest?

18. If the interest of $50, at 8 per cent., is $12, how long has it been on interest?

19. Required the time that $40 must be on interest, at 2 per cent., to gain $8.

20. A gentleman lent $60, at 6. per cent., and received $140; how long was it on interest?

21. A sum of money is on interest at 6 per cent., how long will it take it to double itself?

NOTE. That is, if it gain 6 per cent. a year, how long will it take to gain 100 per cent.?

22. How long will it take a sum of money to double itself, at 9 per cent.? At 18 per cent.? 23. A given principal gains of of itself a year; how long will it take it to double itself?

3

28

NOTE. of = za; if the principal gains of itself in one year, it will take it as many years to gain as much as itself as 28 is contained times in 28, which gives 289

years.

24. A given principal gains of of itself a year; how long will it take to double itself? To gain of itself? of itself?

25. If I loan $1200, at 8 per cent. a year, how long will it be in gaining $80 ?

26. If I loan $500, at 7 per cent. a year, how long will it be in gaining $350 ?

LESSON XLVIII.

1. What principal, in 4 years, at 5 per cent., will amount to $96?

20

NOTE. The interest of any sum of money at 5 per cent., for 4 years, is 10 or of the principal; then the amount is of the principal, for the amount is of the principal, plus the interest,; then, since of the principal = $96, the principal = of $96= $80.

=

2. What is the present worth of $96, due 4 years hence, at 5 per cent.?

NOTE. The present worth of a sum due at some future time is what should be paid now, instead of paying that sum then; it is, therefore, equivalent to a principal which, being put at interest, will amount to the debt at the time of its becoming due.

3. What is the present worth of $50, due in 5 years, at 5 per cent.?

NOTE. That is, what principal, put at interest for 5 years, at 5 per cent., will amount to $50?

4. What is the present worth of $136, due in 6 years, at 6 per cent.?

5. What is the present worth of $172, due in 9 years, at 8 per cent. ?

6. What is the present worth of $71, due in 5 years, at 10 per cent. ?

7. What is the present worth of $78, due in 1 year, at 4 per cent. ?

8. What is the present worth of $85, due in 10 years, at 7 per cent.?

9. What is the present worth of $96, due in 8 years, at 7 per cent.?

10. What is the discount on $100, due in 5 years, at 5 per cent.?

NOTE. Discount is the allowance or deduction made for paying money before it is due; it is equivalent to the interest on the present worth of the debt up to the time of the same becoming payable. The discount, therefore, may be found by subtracting the present worth from the given sum or debt.

11. What is the discount on $84, due in 8 years, at 5 per cent.?

12. What is the discount on $77, due in 9 years, at 6 per cent.?

13. What is the discount on $66, due in 61 years, at 10 per cent.?

14. What is the discount on $74, due in 6 years, at 8 per cent.?

15. What is the discount on $100, due in 2 years, at 7 per cent.?

16. What is the discount on $773, due in 4 years, at 10 per cent. ?

17. What is the discount on $57, due in 2 years, at 7 per cent.?

18. What is the discount on $63, due in 10 months, at 6 per cent.?

19. What is the discount on $75, due in 1 year and 4 months, at 6 per cent.?

LESSON XLIX.

1. Divide a sum of money between A and B, giving A $3 as often as you give B $2; what share of the money will each receive?

NOTE. $3+ $2 = $5; and $3 = 3 of $5, and $2= } of $5. Therefore, A receives, and B of the money.

2. If you divide $15 between A and B, by giving A $3 as often as you give B $2, how many dollars will each receive?

3. Divide $35 between John Wilson and Simon Edwards; how much will each get, if John receive $4 as often as Simon receives $3?