12. In what time will $400 at 6% amount to $460? 13. In what time will $540 at 5% amount to $621?

14. In what time will any principal double itself at 5%? 10%? 20%? 40%? 25%? 50%?

15. In what time will any principal treble itself at 5%? 10%? 20%? 25%? 40%? 163%?

16. In what time will a principal quadruple itself at 5%? 10%? 15%? 20%? 25%? 121%?

17. The amount of a certain principal for a certain time at 5% is $600, and for the same time at 8%, $660; what are the principal and the time?

18. If I invest my money in bank stock yielding a dividend of 10 per cent., it will in a certain time amount to $9000; but if I loan it at 6% for the same time, it will amount to only $7800; what is the amount of money, and what the time?

3.

TO FIND THE PRINCIPAL.

1. What principal will in 6 yr. 6 mo. at 4% give $52 interest?

SOLUTION 1.—6 yr. 6 mo. equals 6 years. The interest on $1 for 61 yr. at 4% is 26 cents; hence $52 is the interest on as many dollars for the given time as 26 cents is contained times in $52, or $200.

SOLUTION 2.-For 6 yr. 6 mo., or 61 yr., at 4%, 3 of the principal equals the interest. Since $52 is 13 of the principal, of the principal is of $52, or $4, and §%, or the principal, is 50 times $4, or $200.

509

2. What principal will in 5 yr. at 4% yield $20 interest? $60? $200? $1200?

3. What principal will in 6 yr. at 5% yield $60 interest? $150? $600? $9?

4. What principal will in 8 yr. at 4% yield $80 interest? $160? $640? $200?

5. What principal will in 6 yr. 8 mo. at 6% yield $100 interest? $120? $640? $1200?

6. A man pays annually on borrowed money $450, at 5% ; how much has he borrowed?

7. How much money has a man on interest at 5%, if his annual income is $1030?

8. A gentleman sold his farm, to be paid for at the end of 1 yr. 4 mo., interest at 6%. When payment was made the amount was $12,960; what was the price of the farm?

9. How much money must be put on interest to amount to $690 in 3 years at 5% ?

10. What principal will in 1 yr. 6 mo. at 8% amount to $224?

11. A debt which has been drawing interest for 6 yr. 4 mo. at 6% amounts to $552; what is the debt?

12. Mr. Williams invested of his money in the lumber trade, and at the end of 2 yr. 6 mo. sold his share for $10,800, at a profit of 8 per cent. yearly gain; how much money had he at first?

PRESENT WORTH.

The Present Worth of a debt is a sum which, if placed on interest at the legal rate for the given time, will amount to the face of the debt when it comes due.

1. What is the present worth of $440, due 2 yr. hence, at 5%?

SOLUTION. Since the amount of $1 for 2 yr. at 5% is $1.10, the present worth of $440 is as many dollars as $1.10 is contained times in $440, or $400.

2. What is the present worth of $420, due 4 yr. hence, at 10%?

3. What is the present worth of $26, due 5 yr. hence, at

11. $600 for 93 da. at 8%. 12. $100 for 63 da. at 8%. 13. $200 for 33 da. at 8%. 14. $600 for 60 da. at 7%. 15. $900 for 63 da. at 7%. 16. $1200 for 95 da. at 6%. 17. $840 for 63 da. at 6%.

18. $660 for 93 da. at 6%. 19. $330 for 93 da. at 8%. 20. $550 for 60 da. at 6%. 21. $600 for 45 da. at 6%. 22. $800 for 63 da. at 6%. 23. $500 for 63 da. at 5%. 24. $400 for 33 da. at 10%.

GENERAL PROBLEMS IN INTEREST.

1.

TO FIND THE RATE.

1. At what per cent. will $200 gain $36 in 3 years?

SOLUTION 1.-The interest on $200 for 1 yr. at 1% is $2, and for 3 yr. it is 3 times $2, or $6. For $200 to gain $36 will therefore require a rate of as many per cent. as $6 is contained times in $36, or 6%.

SOLUTION 2.-At 1% the interest on $1 for 3 years is 3 cents, and on $200 it is 200 times 3 cents, or $6; it will therefore require as many per cent. as $6 is contained times in $36, or 6%.

2. At what per cent. will $300 gain $30 in 2 yr.? 3. At what per cent. will $150 gain $27 in 3 yr. ? 4. At what per cent. will $180 gain $36 in 6 yr.? 5. At what per cent. will $40 gain $16 in 8 yr.? 6. At what per cent. will $250 gain $35 in 3 yr.? 7. At what per cent. will $60 gain $12 in 5 yr.? 8. At what per cent. will $80 gain $10 in 21 yr.? 9. At what per cent. will $90 amount to $108 in 4 yr.? 10. At what per cent. will $500 amount to $605 in 31 yr.? 11. At what per cent. will $30 in 4 yr. 2 mo. amount to $37.50?

12. At what per cent. will $300 in 5

yr. 3 mo. amount to

13. At what per cent. will a principal double itself in 10 yr.? 20 yr.? 4 yr.? 5 yr.? 25 yr.?

NOTE.-In order to double itself it must gain 100%, or once itself. 14. At what per cent. will a principal treble itself in 4 yr.? 5 yr.? 10 yr.? 20 yr.? 25 yr.? 40 yr.?

15. At what per cent. will a principal quadruple itself in 4 yr.? 5 yr.? 10 yr.? 15 yr.? 30 yr.?

16. At what rate will the interest of $600 for 3 yr. 3 mo. 6 days be $102?

17. The amount of a certain principal for 5 years at a certain per cent. is $750, and for 3 years, $690; what are the principal and the rate per cent.?

18. The amount of a certain principal for 4 years at a certain per cent. is $650, and for 7 years, $710; what are the principal and the rate per cent.?

2.

TO FIND THE TIME.

1. In what time will $300 at 6% give $54 interest? SOLUTION.-$300 in 1 year, at 6%, will yield $18 interest, hence to yield $54 will require as many years as 18 is contained times in 54, or 3 years.

2. In what time will $100 at 5% 3. In what time will $200 at 6% 4. In what time will $100 at 4% 5. In what time will $300 at 5% 6. In what time will $140 at 5%

yield $15 interest?
yield $24 interest?
yield $32 interest?
yield $60 interest?
yield $28 interest?
yield $45 interest?

7. In what time will $150 at 6% 8. In what time will $60 at 5% yield $7.50 interest? 9. In what time will $25 at 6% yield $7.50 interest? 10. In what time will $200 at 7% yield $42 interest? 11. In what time will $300 at 6% yield $24 interest?

12. In what time will $400 at 6% amount to $460? 13. In what time will $540 at 5% amount to $621 ?

14. In what time will any principal double itself at 5%? 10%? 20%? 40%? 25%? 50%?

15. In what time will any principal treble itself at 5%? 10%? 20%? 25%? 40%? 163%?

16. In what time will a principal quadruple itself at 5%? 10% 15% 20%? 25%? 12% ?

17. The amount of a certain principal for a certain time at 5% is $600, and for the same time at 8%, $660; what are the principal and the time?

18. If I invest my money in bank stock yielding a dividend of 10 per cent., it will in a certain time amount to $9000; but if I loan it at 6% for the same time, it will amount to only $7800; what is the amount of money, and what the time?

3.

TO FIND THE PRINCIPAL.

1. What principal will in 6 yr. 6 mo. at 4% give $52 interest?

SOLUTION 1.-6 yr. 6 mo. equals 6 years. The interest on $1 for 61 yr. at 4% is 26 cents; hence $52 is the interest on as many dollars for the given time as 26 cents is contained times in $52, or $200.

SOLUTION 2.—For 6 yr. 6 mo., or 61 yr., at 4%, }} of the principal equals the interest. Since $52 is 13 of the principal, of the principal is of $52, or $4, and 38, or the principal, is 50 times $4, or $200. 2. What principal will in 5 yr. at 4% yield $20 interest? $60? $200? $1200?

3. What principal will in 6 yr. at 5% yield $60 interest? $150? $600? $9?

4. What principal will in 8 yr. at 4% yield $80 interest? $160? $640? $200 ?