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388. Banking is the general business transacted at banks.
A bank is a joint-stock company, established for the purpose of receiving deposits, loaning money, dealing in exchange, or issuing bank-notes or bills, as a circulating medium, redeemable in specie at its place of business.
The capital of a bank is the money paid in by its stockholders, as the basis of business.
The affairs of a bank are usually managed by a board of directors chosen by the stockholders, and the principal officers are a president, a cashier, and one or more tellers.
NOTE. — The president and cashier sign the bills issued; the cashier superintends the bank accounts; and the tellers receive and pay out money. A bank check is an order drawn on the cashier for money.
389. Bank discount is the simple interest of a note, draft, or bill of exchange, deducted from it in advance, or before it becomes due.
The interest is computed, not only for the specified time, but for three days additional, called days of grace.
The legal rate of discount is usually the same as the legal rate of interest; and the difference between bank discount and true discount is the same as the difference betoveen interest and true discount (Art. 384).
390. A note is said to be discounted at a bank, when it is received as security for the money that is paid for it, after deducting the interest for the time until it becomes due.
The money paid for a note is called its avails, proceeds, or
391. A note, though nominally due at the time specified in it, is not legally due till the days of grace have been counted.
The time a note has to run is counted in days from after the day of its being discounted to the day of its becoming legally due.
392. To find the bank discount and the avails or proceeds of a note or bill for any time or rate per cent.
Ex. 1. What is the discount on a note for $ 1000 having 63 days to run, discounted at a bank at 6 per cent. ? How much are the proceeds ? Ans. Discount, $10.50; proceeds, $ 989.50.
We find the interest Sum discounted,
$1 0 0 0.0 0 on the sum discounted
as in Art. 354, and this ido of sum = int. for 60d. 1 0.0 0
interest is the bank 26 of int. for 60d. int. for 3d. .50 discount (Art. 389), Bank discount,
$ 1 0.5 0
which subtracted from the
discounted Proceeds, or present worth, $9 89.5 0 gives the proceeds or
present worth. Hence, Find the interest on the note, or sum discounted, for the given rate and time, including THREE days of grace, and this interest will be the discount.
Subtract the discount from the face of the note, or sum discounted, and the remainder will be the proceeds, or present worth.
2. What is the bank discount on a note for $ 7800 on 90 days' time?
Ans. $ 120.90. 3. What is the bank discount on a note for $ 1200, payable in 60 days, at 7 per cent. ?
Ans. $ 14.70. 4. What is the bank discount on $ 8000, payable in 60 days? What are the proceeds ?
Ans. Discount, $ 84 ; proceeds, $ 7916. 5. How much money should be received on a note for $ 760, payable in 5 months, discounted at a bank ?
6. A merchant sold a cargo of hemp for $7860, for which he received a note payable in 6 months.
How much money will he receive at a bank for this note ? Ans. $ 7620.27.
7. If the following note was discounted April 3, 1857, how long had it to run, and what were the proceeds ? $ 160-18%
Boston, December 3, 1856. Six months after date, for value received, we promise to pay Robert S. Davis & Co., or order, one hundred and sixty Mono dollars, at the Merchants' Bank.
HALLETT, OsGOOD, & Co. Ans. 63 days; proceeds, $ 158.72.
8. Required the time when the following note will become legally due, and the bank discount, provided it was discounted May 16, 1856, the rate being 7 per cent. $ 89013
Chicago, April 16, 1856. One hundred and twenty days after date, I promise to pay to the order of Keen and Lee eight hundred and ninety Podollars, at the Marine Bank.
THOMAS L. Cook. Ans. August 17, 1856; discount, $ 16.103. 9. Required the legal time of maturity of the following note, and the proceeds, it having been discounted June 11, 1856. $ 1340.
Philadelphia, May 1, 1856. For value received, ninety days after date, we promise to pay J. B. Lippincott & Co., or order, one thousand three hundred and forty dollars, at the Girard Bank, without defalcation.
Johnson & Pollock. 10. The following note was discounted, at 2 per cent. a month, July 5, 1857 ; how long had it to run, and what were the proceeds? $ 9000.
New York, June 19, 1857. Two months after date, for value received, I promise to pay to the order of Joseph Appleton, nine thousand dollars, at the Manhattan Bank.
L. T. ROBERTS.
Ans. 48 days ; proceeds, $ 8712.00. 393. To find the amount for which a note must be given that the proceeds shall be a specified sum.
Ex. 1. For what amount, payable in 60 days, must a note be given to a bank discounting at 6 per cent., to obtain $ 989.50 ?
Ans. $ 1000.
Since $0.9895 of pro
$ 1.0 0 0 0 ceeds requires $ 1 to be Interest of $ 1 for 63 days, .010 5 discounted, $ 989.50 will
require as many dollars Proceeds of $ 1,
$ 0.9 8 9 5
as $ 0.9895 is contained
times in $ 989.50, $ 989.50 = .9895 = $ 1000.
$ 1000. Hence, Divide the given sum by the proceeds of $1 for the given time and rate of bank discount, including THREE days of grace, and the quotient will be the required amount.
2. What sum, payable in 90 days, if discounted at 7 per cent. bank discount, will produce $ 680 ? Ans. $ 692.52.
3. What must be the face of a note, which, when discounted at a bank for 120 days, shall give as its proceeds $ 540.50 ?
Ans. $ 551.81. 4. For what amount must a note be given, in order that the proceeds of the note discounted, when having 6 months to run, shall be $ 1938 ?
5. The avails of a note, having 4 months to run, discounted at a bank, were $ 1631.60; what was the face of the note?
Ans. $ 1665.74. 6. If a gentleman wishes to obtain $ 1500, for what sum must he give his note payable in 30 days, allowing it is to be discounted at 1 per cent. a month ?
Ans. $ 1516.68. 394. To find the rate of interest corresponding to a given rate of bank discount.
Ex. 1. What rate of interest is paid when a note payable in 60 days is discounted at 6 per cent. ?
Ans. 61996 per cent.
Every $ 1 discounted for the given .06 ; .9895
time and rate yields as its proceeds
$ 0.9895. Then, if $ 1 in the given time yield a certain interest at 6 per cent., $ 0.9895 in the same time will yield the same interest, at as many per cent as the given rate, .06, contains times .9895.
RULE. – Divide the given rate per cent., expressed decimally, by the number denoting the proceeds of $ 1 for the given time and rate. The quotient will be the rate of interest required.
2. What rate of interest is paid when a note payable in 30 days is discounted at 6 per cent. ? Ans 61666 per cent.
3. What rate of interest is paid when a note payable in 90 days is discounted at 6
cent. ? Ans. 648.85 per cent. 4. A note payable in 4 months is discounted at 2 per cent. a month ; what rate of interest is paid ?
5. When a note, payable in 6 months, is discounted at 7 per
cent., to what rate of interest does the bank discount correspond?
6. When a note payable in one year, without grace, is discounted, to what rate per cent of interest does the bank discount correspond ?
Ans. 649 per cent. 395. To find the rate of bank discount corresponding to a given rate of interest.
Ex. 1. At what rate of bank discount must a note, payable in 60 days, be discounted, to produce 6 per cent. interest?
Ans. 5.189 í per cent.
Since bank discount is reckoned .06 • 1.0105 = .051821. on an amount which equals the pro
ceeds plus the interest on the preceeds for the given time and rate (Art
. 389), the bank discount for every $ 1 of proceeds equivalent to the interest on $1+.0105
$ 1.0105. Then, if $ 1 yield a certain interest in a given time at 6 per cent. per annum, $ 1.0105 must yield the same interest in the same time, at as many per cent. per annum as the given rate, .06, contains times 1.0105.
Rule. - Divide the given rate per cent., expressed decimally, by the number denoting the amount of $ 1 for the given time and rate. The quotient will be the rate of bank discount required.
2. At what rate must a note, payable in 30 days, be discounted, to produce 6 per cent. interest?
Ans. 51:41 per cent. 3. At what rate must a note, running 60 days, be discounted, to yield 2 per cent. a month interest? Ans. 23 771 per cent.
4. At what rate must a note, running 90 days, be discounted, to produce 6 per cent. interest ?
5. At what rate must a note, running 120 days, be discounted, to produce 8 per cent. interest?
6. At what rate must a note, running 6 months, be discounted, to produce 7 per cent. interest?
7. At what rate must a note, payable 1 year hence, without grace, be discounted, to produce 6 per cent. interest ?
8. What rate of bank discount on a note, payable 8 years and 4 months hence, without grace, corresponds to 5 per cent interest ?
Ans. 347 per cent.