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580. ILLUSTRATIVE EXAMPLE. What is the bank discount of a note for $ 400, payable in 90 days, discount at 7%? What are the proceeds ?
Explanation. - Bank discount is in$ 400
terest for the specified time and 3 days
The interest of $ 400 for 93 days at 6) 6.2000
7% is $ 7.23, the discount. $ 400 less 1.0333
$ 7.23 equals $392.77, the proceeds of $ 7.2333
the note. $ 400 - $7.23 = $392.77.
Ans. $ 7.23 discount; $ 392.77 proceeds.
581. From the above may be derived the following
I. To find bank discount on a note due at a future time, without interest: Compute interest on the face of the note from the time of discount to maturity (including the three days of grace).
II. To find the proceeds of the note: Subtract the discount from the face of the note.
Note. When a note drawing interest is discounted, the discount is computed upon the amount of the note at the time of its maturity.
582. Examples for the Slate. 99. What is the bank discount of a note for $ 750, payable in 30 days, discount 6% ? What are the avails ?
Find the bank discount and proceeds of a note 100. For $ 1000, payable in 90 d., discount 7 %. 101. For $ 300, payable in 4 mo., discount 8%.
102. For $ 700, dated Dec. 10, payable in 69 days, and discounted at date at 10%.
103. For $ 500, dated Aug. 20, payable in 3 mo., and discounted at date at 7} %.
Find the bank discount and proceeds of a note
104. For $290, dated Dec. 30, 1877, payable in 2 mo., and discounted at date at 9%.
105. For $500, dated May 10, payable in 90 days, and discounted June 9 at 6%.
106. For $256.84, dated Oct. 28, payable in 60 days, and discounted Nov. 12 at 12%.
107. For $1200, dated Jan. 31, payable in 3 months, and discounted March 8 at 5%.
108. I bought a horse and carriage for $324, for which I gave my note Nov. 5, payable in 1 year, with interest at 6%. What would be the avails of this note at a bank, Aug. 1, discount 7%?*
109. Find the bank discount and avails of the following note, discounted Feb. 12, 1876, at 10%. $ 4000.
SAN FRANCISCO, Nov. 7, 1875. Six months from date, with interest at 10%, I promise to pay F. Egleston & Co., or order, Four Thousand Dollars
; value received.
583. ILLUSTRATIVE EXAMPLE. For what sum must a note be drawn, payable in 60 days, without interest, that the avails may equal $ 591.60 when the note is discounted at a bank at 8% ?
Explanation. - The Bank discount of $1 for 63 d. = $ 0.014 bank discount of $1 for Avails of $1 for 63 d.
0.986 63 days at 8% is $0.014; $ 591.60 = $0.986
hence, the avails of $1
discounted will be $ 1 Ans. $ 600.
minus $0.014, which equals $0.986. Since the avails of $1 are $0.986, that the avails may be $591.60 the note must be drawn for as many dollars as there are times $0.986 in $591.60, which is 600. Ans. $ 600.
* See Art. 581, note.
584. From the foregoing may be derived the following
Rule. To find the face of a note which discounted at a bank will yield given proceeds : Divide the given proceeds by the proceeds of 1 dollar for the given rate and time, with 3 days of grace.
NOTE. To find the face of the note when the discount is given : Divide the given discount by the discount of $1 for the given rate and time, with 3 days of grace.
585. Examples for the Slate. 110. For what sum must a 30 days' note, without interest, be drawn that the avails at 6% discount may be $ 80 ?
111. For what must a 4 months' note, without interest, be drawn that when discounted at a bank it may yield $ 489.75 at 6% discount?
112. What must be the face of a note given for 90 days, without interest, that the avails at a bank may be $1469, discount being 8%?
113. What was the face of a note given for 45 days, not bearing interest, on which the bank discount at 9 % was $11.40?
586. Miscellaneous. 114. What difference does it make in the avails of a note for $200, payable without interest in 18 months, whether it be reckoned by true or by bank discount, rate 8% ?
115. What will be the difference between the true and the bank discount of a note for $9171, payable May 9, 1878, and discounted Jan. 15, 1878, at 6% ? $ 500.
RICHMOND, Oct. 5, 1876. For value received, I promise to pay Charles Towle, or order, Five Hundred Dollars in three months. JAMES ALLEN.
116. What cash must be paid to discharge the above note at its date by true present worth, rate of interest 6%?
117. What would be the avails of it at a bank, Dec. 5, 1876 ?
118. What would be the amount of it, March 17, 1877 ? 119. What would be the true discount of it, Nov. 5, 1876 ? 120. What would be the bank discount of it, Nov. 5, 1876 ? For other examples in bank discount, see page 253.
587. Business men are usually allowed a deduction for making cash payment for goods purchased on time. Notes also not bearing interest are discounted by the deduction of a certain per cent, not wholly depending upon the time. Such a deduction is called business or commercial discount.
588. Examples for the Slate. 121. A merchant bought a lot of goods amounting to $ 124, on 30 days' credit; 5% discount on the price was allowed for making payment at the time of purchase. What was paid ?
122. A man having bought a bill of goods amounting to $ 468.20 on 6 months' time, cashed the bill for 10% off. What did he pay ?
123. What is the cash value of a bill of cloth amounting to $ 347.20, on the face of which a discount of 6% is made, and on the balance another of 5%?
124. What is the difference between discounting a bill of $ 1000 at 33}% and taking 10% off from the remainder, and discounting the whole bill at 43}%?
125. A person paid $ 1.14 per yard for goods after a discount of 5% had been made upon the invoice price. What was the invoice price? NOTE. Since 5% had been deducted, 95% remained.
126. What was the invoice price of a lot of French plateglass for which I paid $39 per pane after a discount of 40% had been made ?
127. If from the retail price of a book 20% is deducted, and a discount of 10% made
upon the balance, and then the book sells for $1.33, what is the retail price ?
589. A sum of $ 500 was loaned at 7%, interest payable annually. At the end of the first year the interest for that year was added to the principal, and upon the amount as a new principal the interest was reckoned for the second year. The amount for the second year formed a new principal, upon
which interest was reckoned for the next six months, at the end of which time the note, with interest, was paid. What was the amount then due? What was the interest gained ?
$ 592.49 1st Ans.
$ 92.49 2d Ans.
590. Interest upon both interest and principal, the sum of the two forming a new principal for specified periods of time, is compound interest.
In the example above the interest is compounded annually. It may be compounded semi-annually, or for any period of time agreed upon.
591. From the operation above may be derived the following
1. Find the amount of the given principal for the first period of time. With this as a new principal, find the