1. Find the accurate interest of $1560 for 45 da. at 7%.

2. Find the exact int. of $1600 for 1 yr. 3 mo. at 6%.

3. What is the difference between the exact interest ci $646.40 at 8% for 1 yr. 3 mo. 20 da. and the interest reckoned by the 6% method?

4. Find the exact interest of $875.60 at 7% for 63 da. 5. Required the exact interest on three U. S. Bonds of $1000 each, at 6%, from May 1 to Oct. 15.

6. What is the exact interest on a $500 U. S. Bond, at 5%, from Nov. 1 to April 10 following?

575. Find the interest, by any of the ordinary methods,

1. Of $721.56 for 1 yr. 4 mo. 10 da. at 6%.

2. Of $54.75 for 3 yr. 24 da. at 5%.

3. Of $1000 for 11 mo. 18 da. at 7%.

4. Of $3046 for 7 mo. 26 da. at 8%.

5. Of $1821.50 from April 1 to Nov. 12 at 6%.
6. Of $700 from Jan. 15 to Aug. 1 at 10%.
7. Of $316.84 from Oct. 20 to March 10 at 7%

What is the amount

8. Of $3146 for 2 yr. 3 mo. 10 da. at 7%? 9. Of $96.85 for 3 yr. 1 mo. 27 da. at 6% ?

10. Of $1008.80 for 10 mo. 16 da. at 61%? 11. Of $2000 for 15 da. at 121%?

12. Of $137.60 for 127 da. at 10%?

13. If $1671.64 be placed at interest June 1, 1874, what amount will be due April 1, 1876, at 7% ?

14. How much is the interest on a note for $600, dated Feb. 1, 1872, and payable Sept. 25, 1875, at 6%?

15. If a man borrow $9700 in New York, and loan it in Colorado, what will it gain at legal int. in a year ? 16. Required the interest of $127.36 from Dec. 12, 1873, to July 3, 1875, at 41%.

17. A note of $250, dated June 5, 1874, was paid Feb. 14, 1875, with interest at 8%. What was the amount?

18. A note for $710.50, with interest after 3 mo., at 7%, was given Jan. 1, 1874, and paid Aug. 12, 1876. What was the amount due?

19. A man engaged in business was making 121% annually on his capital of $16840. He quit his business and loaned his money at 71%. What did he lose in 2 yr. 3 mo. 18 da. by the change?

20. A man borrows $2876.75, which belongs to a minor who is 16 yr. 5 mo. 10 da. old, and he is to retain it until the owner is 21 years old. What will then be due at 8% simple interest?

21. A speculator borrowed $9675, at 6%, April 15, 1874, with which he purchased flour at $6.25. May 10, 1875, he sold the flour at $7 a barrel, cash. What did he gain by the transaction?

22. A man borrows $10000 in Boston at 6%, reckoning 360 da. to the year, and lends it in Ohio at 8%, reckoning 365 da. to the year. What will be his gain in 146 days?

23. A tract of land containing 450 acres was bought at $36 an acre, the money paid for it being loaned at 51%. At the end of 3 yr. 8 mo. 24 da., of the land was sold at $40 an acre, and the remainder at $38 an acre. What was gained or lost by the transaction ?

PROBLEMS IN INTEREST.

576. Interest, time, and rate given, to find the principal.

1. What sum of money will gain $10 in 1 yr. at 5%? ANALYSIS.—The interest of $1 for 1 yr. at 5% is .05 of the principal, and therefore $10.05, or $200, is the required sum. Or,

Since $.05 is the interest of $1, $10 is the interest of as many dollars as $.05 is contained times in $10, or 200 times. Hence, etc.

577. 1. What sum of money, put at interest 31 yr. at 6%, will gain $346.50 ?

2. Will gain $49.50 in 1 yr. 3 mo. at 6%? At 5%? 3. Will gain $153.75 in 3 mo. 24 da. at 7%? At 8%?

RULE.-Divide the given interest by the interest of $1 for the given time, at the given rate.

FORMULA.-Principal Interest ÷ (Rate × Time).

What sum of money

=

4. Will gain $213 in 5 yr. 10 mo. 20 da. at 7%?

5. Will gain $173.97 in 4 yr. 4 mo. at 6%? At 12% ?

6. A man receives semi-annually $350 int. on a mortgage at 7%. What is the amount of the mortgage?

578. Amount, rate, and time given, to find the principal.

1. What sum of money will amount to $107 in 1 yr. at 7%?

ANALYSIS.-Since the interest is .07 of the principal, the amount is 1.07, or 187, of it. If $107 is 107 of the principal, of the principal is of $107, or $1; and 188, or the principal itself, is $100. Or, Since $1.07 is the amount of $1, $107 is the amount of as many dollars as $1.07 is contained times in $107, or $100.

579. 1. What sum will amount to $337.50 in 5 yr.

3. Will amount to $1596 in 2 yr. 6 mo. at 51%?

4. Will amount to $1531.50 in 3 mo. 18 da. at 7%?

RULE.-Divide the given amount by the amount of $1 fr the given time, at the given rate.

FORMULA.-Prin. Amt.÷(1+ Rate x Time).

35

5. What is the principal which in 217 days, at 51%, amounts to $918.73?

6. What principal in 3 yr. 4 mo. 24 da. will amount to $761.44 at 5%?

580. Principal, interest, and time given, to find the rate.

1. At what rate will $100 gain $14 in 2 years?

ANALYSIS.—Since the interest of $100 is $14 for 2 yr., it is $7 for 1 yr., and $7 is .07 of $100, the principal. Hence the rate is 7%. Or, Since the interest of $100 for 2 yr. at 1% is $2, $14 is as many per cent. as $2 is contained times in $14, or 7%.

581. 1. At what rate per cent. will $1600 gain $280

2. Will $2085 gain $68.11 in 5 mo. 18 da. ?

3. Will $1500 gain $252 in 2 yr. 4 mo. 24 da. ?

KULE.-Divide the given interest by the interest of the given principal, for the given time, at 1%.

FORMULA.-Rate Int.

(Prin. x 1% x Time).