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Find the exact interest on:

19. $850 from Jan. 15, 1904, to June 20, 1904, at 8%. 20. $125 from Jan. 20, 1905, to Nov. 19, 1905, at 6%.

21. On what date, counting from Jan. 15, will $200 at 6% produce as much accurate interest as it would ordinary interest from Jan. 15 to Sept. 15?

Miscellaneous:

22. What principal at 6% will amount to $450 in 5 years? 23. Mr. Roe borrowed $1575 on the 1st of April. On the 1st of November following he paid the amount, which was $1630.125. What rate of interest did he pay?

24. In what time will any principal double itself at 8%? 25. At what rate will any principal double itself in 12 years?

26. What is the difference between the true discount of $248.76, due in 2 yr. 3 mo. 15 da., and the simple interest on the same amount for the same time, money being worth 6%?

27. A note of $87.50, dated Aug. 8, 1901, and bearing interest at 10%, was paid March 25, 1903. What was the amount paid?

28. Find the amount of $63.96 for 1 yr. 7 mo. 10 da., at 61%.

29. What is the interest on a note of $600, dated June 10, 1900, and paid Jan. 3, 1901, at 5% interest?

30. A man who has $1650 in a savings bank receives $41.25 every 6 months. What per cent interest does he receive on his money?

THREE IMPORTANT RULES:

1. To find the simple interest:

Multiply the principal by the rate and the result by the time expressed in years, and the result will be the simple interest.

2. To find the present worth:

Divide the debt by the amount of $1 for the given time and rate, and the quotient will be the present worth. 3. To find the true discount:

Subtract the present worth from the debt, and the remainder will be the true discount.

II. BANK DISCOUNT

345. A bank is an institution authorized by law for the safe-keeping, loaning, and issuing of money.

346. Bank discount is the sum deducted by a bank for paying a note or draft before it is due, or the sum charged for lending money. It is simple interest on the maturity value of a note or draft for the time it has yet to run.

347. The term of discount is the time from the date of discount to, and including, the date of maturity.

348. The date of maturity is the last day of grace (in states allowing 3 days of grace) or the day on which the note is legally due.

NOTE 1.—Many of the states have abolished the law allowing 3 days of grace. For your own state, see table, p. 159.

NOTE 2.-Notes falling due on a legal holiday, or on Sunday, mature and are payable on the preceding or succeeding business day, according to the law or custom of the locality. See p. 159.

349. The proceeds (called also net proceeds) of a note or draft is the difference between the maturity value and the bank discount.

NOTE.-In bank discount, 3 days of grace are considered in this book.

1. Find the bank discount and proceeds of a note of $500, due in 90 days, discounted at 8%.

EXAMPLES

SOLUTION:

1. The term of discount

93 days.
2. $500 × 180 × 3 = $10.33
3. $500 $10.33 $489.66 = proceeds.

Step 2 may be analyzed as in example 1 in simple interest.

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bank discount.

2. I wish to borrow $1800 for 90 days. For what sum must the note be made, if the bank discounts it at 8%?

SOLUTION:

1. The discount on $1 for 93 days = $0.021.
2. The proceeds on $1 for 93 days = $0.9713.
3. $1800 $0.971 · 1837.985.
4. .. the note must be made for $1837.985.

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3. $1100.

MARLIN, TEX., July 5, 1904.

Three months after date, I promise to pay David Doe, or order, eleven hundred dollars, at the Merchants' National Bank, with interest at 6%. Value received.

JOHN ROE.

Discounted Aug. 5, 1904.

SOLUTION:

1. This note matures Oct. 5 + 3 days, or Oct. E.
2. The int. on $1100 for 93 days at 6% = $17.05.

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3. $1100 + $17.05 $1117.05

the maturity value.

4. The term of discount is from Aug. 5 to Oct. 8, or 64 days. 5. The int. on $1117.05 for 64 days at 6% $11.92=bank discount. 6. $1117.05 $11.92 = $1105.13, the proceeds.

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Exercise XLI

Find the bank discount and proceeds of a note: 1. Of $386, due in 100 days, discounted at 6%. 2. Of $36.20, payable in 80 days, discounted at 5%. 3. Of $850, payable in 90 days, discounted at 7%. 4. A merchant is offered $3000 worth of goods on 3 months' time, or 5% off for cash. If he borrows the money at the bank, at 7%, and pays cash, will he gain or lose, and how much?

5. A man borrows $1000 for 60 days; bank discount is 8%. Find the face of the note.

6. A note of $600 dated July 28, at 3 months, was discounted at bank Sept. 5, at 8%. Find the proceeds.

7. $1200.

SPRINGFIELD, ILL., Aug. 5, 1903.

Ninety days after date, I promise to pay Tom Johnson, or order, twelve hundred dollars, for value received, at the City National Bank.

BILL WILLIAMS. Find the proceeds, if discounted Sept. 2, 1903, at 8%. 8. $640. MACON, GA., March 10, 1903.

Five months after date, I promise to pay to the order of Henry Babb, six hundred forty dollars, for value received, with interest at 6%.

M. P. RYE.

Find the proceeds, if this note was discounted at the bank, at 8%, May 29, 1903.

9. My note of $360, which will be legally due in 1 yr. 4 mo. 20 da., is discounted at a bank, at 8%. What rate of interest does the banker receive?

NOTE. The difference between true discount and bank discount is equal to the simple interest on the true discount for the given time at the given rate. Illustrate this fact by solving the following example:

10. Find the difference between the true discount and the bank discount on $440, due in 1 yr. 8 mo., at 6%, not reckoning days of grace.

III. ANNUAL INTEREST

350. Annual interest is simple interest on the principal, augmented by the simple interest on each interval's interest from the close of the interval to the time of settlement.

EXAMPLE

A note of $600.00 drawing 6% interest, payable annually, runs for 4 years and 3 months. Find the amount due at maturity, if no payments have been made.

SOLUTION:

Each year's interest will bear interest after it becomes due, as follows:

1. 1st year's interest for 3 years, 3 months.

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2. 2d year's interest for 2 years, 3 months.
3. 3d year's interest for 1 year, 3 months.
4. 4th year's interest for 0 years, 3 months.

Total

7 years.

To the simple interest on the principal for 4 years, 3

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