.15)3.0020Ans.20%Here, $15.00 is the base, and ($18 - $15) $3.00, the gain or percentage. Now, as 1% of 15.00 is .15, it is evident that 3.00 is as many per cent of 15.00, as .15 is contained times is 3.00, which is 20.
.15)3.0020Ans.20%
Here, $15.00 is the base, and ($18 - $15) $3.00, the gain or percentage. Now, as 1% of 15.00 is .15, it is evident that 3.00 is as many per cent of 15.00, as .15 is contained times is 3.00, which is 20.
Proof: 20% or1⁄5of $15 = $3.
The percentage and rate given, to find the base.
Rule.—Divide the percentage by the rate per cent expressed decimally.
Example: Received $6.40, percentage or interest, for money loaned at 4%, what was the base or principal?
.04)6.40Ans.$160If $1 produces .04 (4 cents) in a certain time, $6.40 must be the percentage of as many dollars as .04 is contained times in $6.40, which is 160.
.04)6.40Ans.$160
If $1 produces .04 (4 cents) in a certain time, $6.40 must be the percentage of as many dollars as .04 is contained times in $6.40, which is 160.
Proof: 4% of $160 (160 × .04) = $6.40.
The amount and rate given, to find the base.
Rule.—Divide the given amount by 1.00 plus the rate per cent.
Example: Bought a horse at a certain price, and sold him for $84, making 12% on cost; what did he cost?
1.12)84.00Ans.$75If I made 12% on cost, every dollar invested gained 12 cents; hence, the horse cost as many dollars as 1.12 is contained times in 84.00, which is 75.
1.12)84.00Ans.$75
If I made 12% on cost, every dollar invested gained 12 cents; hence, the horse cost as many dollars as 1.12 is contained times in 84.00, which is 75.
Proof: 12% of $75 (75 × .12) = $9; $75 + $9 = $84.
The proceeds and the rate given, to find the base.
Rule.—Divide the given proceeds by 1.00 minus the rate per cent.
Example: Sold a wagon for $51, which is 40% less than it cost; what did it cost?
.60)51.00Ans.$85If I lost 40%, or 40 cents on the dollar, I received only 60 cents for every dollar the wagon cost; hence, it cost as many dollars as .60 is contained times in 51.00, which is 85.
.60)51.00Ans.$85
If I lost 40%, or 40 cents on the dollar, I received only 60 cents for every dollar the wagon cost; hence, it cost as many dollars as .60 is contained times in 51.00, which is 85.
Proof: 40% of $85 (85 × .40) = $34; $85 - $34 = $51.
Note.—The principles of percentage, in one form or another, enter into nearly all commercial calculations, besides many others. It is therefore of the utmost importance to business men, clerks, accountants, bookkeepers, and others, to become expert in percentage, and to adopt the easiest, simplest and shortest methods in computing interest, partial payments, trade discount, profit and loss, commission, insurance, stocks, bonds, taxes, exchange, etc.
When a thing is sold for more than it cost the seller, it is said to be sold at a profit. If it is sold for less than the cost, it is sold at a loss. Hence,
A profit or loss is generally reckoned as a percentage.
It is always understood that the percentage is reckoned on the cost price.
Example: I buy wheat at 60 cents and sell it for 75 cents. What per cent do I gain?
Solution: I gain the difference between 75 cents and 60 cents, or 15 cents. 15 cents is 25% of the cost. Hence, I gain 25%.
Work:
Example: I bought flour at $3.50 per barrel. For what must I sell it to gain 20%?
Solution: I must sell it for 100% of the cost plus 20% of the cost, or 120% of the cost.
120% of $3.50 = $4.20.
∴ I must sell it at $4.20.
Example: I sold my carriage for 80% of its cost and received $90 for it. What was the cost?
Solution:
1% of the cost is1⁄80of $90, or $1.125.
100% of the cost = 100 × $1.125, or $112.50.
is a percentage paid for buying or selling real estate, goods, etc. A consignment is a quantity of goods, sent to an agent, broker or commission merchant, for sale. The consignor is the one who sends the goods, the consignee the one to whom they are sent.
Principles:
1.The commission is some number or per cent of the price of what is bought or sold.
2.The proceeds equal the selling price minus the commission.
3.The amount equals the selling price plus the commission.
Commission presents two classes of problems. One of these classes may be called “buying problems.” The other may be called “selling problems.”
Buying Problem: I sent my agent $1977.60 tobuywild farm lands in northern Wisconsin, at $3 per acre. He was to receive 3% for his work. How many acres did he buy?
Work and Explanation:
3% of $3 = $.09.Cost to me of 1 acre is $3 + .09 = $3.09
For $1977.60 he buys as many acres as $3.09 is contained times in $1977.60, or 640. Hence, he buys 640 acres.
Selling Problem: My agentsells360 pounds of butter for me at 20 cents. He pays $4.20 freight charges and $9.60 for storage. His commission is 5%. What does he send me?
Work and Explanation:
is an allowance made by manufacturers and jobbers from their list or marking prices. When the market varies, they change the discount accordingly, or make several discounts instead of changing the list.
Trade discount is a certain per cent off, or from list or marking price; while profit and loss is computed on the cost or purchase price.
The amount of the discount allowed depends sometimes upon the amount of order, and sometimes upon the terms of settlement. Very often two or more discounts are deducted in succession. Thus, 10% and 5% off; or, as it is generally[872]expressed in business, 10 and 5 off, means a discount of 10%, and then 5% from what is left; 20, 10, and 5 off, means three successive discounts. A retailer’s profit is smaller when he is allowed 10 and 5 off, than if he were allowed 15 off. The result is not affected by the order in which the discounts are taken.
Example:I receive a bill of goods amounting to $100, 20% off. What is the net cost?
First Way:
20% of $100 =$20$100 - $20 = $80
Second Way:
100% - 20% = 80%80% of $100 = $80
Example:A merchant receives two bills of $200 each. On one there is a discount of 25%; on the other, 15% and 10%. What must he pay on each, net?
First Bill:
100% - 25% = 75%, or3⁄43⁄4of $200 = $150.
Second Bill:
100% - 15% = 85%100% - 10% = 90%90% of 85% = 76.5%.765 × $200 = $153.
Anoteis a written promise to pay a specified sum at a certain time.
The person who promises is called themaker, and the person to whom he promises is called thepayee.
TheFACEof a note is the sum of money promised.
Anegotiable noteis one which is made payable to the bearer, or to the order of the payee. A negotiable note can be sold or transferred.
A note isnon-negotiablewhen it is payable only to the person or persons named in the note.
Anindorserof a note is a person who writes his name on the back of it. The person who indorses, by so doing guarantees its payment. Anindorsement in blankis simply the signature of the indorser written across the back of the note or draft. When indorsed in this way the note or draft is made payable without further indorsement to any person holding.
A note or draft isindorsed in fullwhen the indorser states, over his signature, the person to whose order the note or draft is to be paid. If an indorser does not wish to guarantee the payment of a note or draft, he writes “Without recourse” over his name when indorsing it.
Aprotestof a negotiable note or draft is a formal statement by a notary public that said note or draft was presented for payment or acceptance and refused.
A note, when due, must be presented at the place at which it is made payable. Theday of maturityis the day on which a note becomes due.
Thedays of graceare the three days beyond the specified time for payment. Days of grace are now practically abolished throughout the United States.
Kinds of Notes.—There are three principal kinds of notes—Time Notes,Joint Notes,andJoint and Several Notes.
ATime Notemust be paid in a specified time.
AJoint Noteis one signed by two or more persons who are jointly liable for its payment.
AJoint and Several Noteis a note signed by two or more persons who are both jointly and individually liable for its payment. Each man who signs the note is as much responsible for the payment of the whole sum as if he had signed alone.
A note made out onSundayis void.
If a note does not state thatinterestis to be paid, it does not bear interest until after it is due.
If anyone obtains a noteby fraudor from anintoxicated person,he cannot collect.
To be negotiablean instrument must be in writing and signed by the maker (of a note) or drawer (of a bill or check).
It must containan unconditional promise or order to pay a certain sum in money.
Must be payable on demand, or at a fixed future time.
Must be payable to order or to bearer.
In a bill of exchange (check), the party directed to pay must be reasonably certain.
Every negotiable instrument is presumed to have been issued for a valuable consideration, and want of consideration in the creation of the instrument is not a defense against a bona-fide holder.
An instrument is negotiated, that is completely transferred, so as to vest title in the purchaser, if payable to bearer, or indorsed simply with the name of the last holder, by mere delivery; if payable to order, by the indorsement of the party to whom it is payable and delivery.
One who transfers an instrument by indorsement warrants to every subsequent holder that the instrument is genuine, that he has title to it, and that if not paid by the party primarily liable at maturity, he will pay it upon receiving due notice of non-payment.
To hold an indorser liablethe holder upon its non-payment at maturity must give prompt notice of such non-payment to the indorser and that the holder looks to the indorser for payment. Such notice should be sent within twenty-four hours.
When an indorser is thus compelled to payhe may hold prior parties, through whom he received the instrument, liable to him by sending them prompt notice of non-payment upon receiving such notice from the holder.
One who transfers a negotiable instrument by delivery, without indorsing it, simply warrants that the instrument is genuine, that he has title to it, and knows of no defense to it, but does not agree to pay it if unpaid at maturity.
The maker of a note is liableto pay it, if unpaid at maturity, without any notice from the holder or indorser.
Notice to one of several partners is sufficient notice to all.
When a check is certifiedby a bank the bank becomes primarily liable to pay it without notice of its non-payment, and when the holder of a check thus obtains its certification by the bank, the drawer of the check and previous indorsers are released from liability, and the holder looks to the bank for payment.
A bona-fide holderof a negotiable instrument, that is, a party who takes an instrument regular on its face, before its maturity, pays value for it and has no knowledge of any defenses to it, is entitled to hold the party primarily liable responsible for its payment, despite any defenses he may have against the party to whom he gave it, except such as rendered the instrument void in its inception. Thus, if the maker of a note received no value for it, or was induced to issue it through fraud or imposition, that does not defeat the right of a bona-fide holder to compel its payment from him.
The dates and amounts ofpartial paymentson a note, before it is finally paid in full, are placed on the back.
Theplace of payment, if not mentioned, is at the maker’s place of business or residence, during reasonable business hours.
If anoteor acheckreceived in payment of a debt isdishonored, the debt revives.
Ignoranceof the law does not excuse anyone. Nocontractis good unless there be aconsideration. No consideration is good that isillegal.
Themakerof anaccommodation noteis not bound to the person accommodated; but he is bound to any other person receiving the note for value.
The sum charged by abankfor cashing a note or time draft is calledbank discount. This discount is the simple interest, paid in advance, for the number of days the note has to run. Wholesale business houses usually sell goods ontimeand take notes from the retailers in payment. These notes are not often for a longer period thanthree months. Some are placed in the banks for collection, others arediscounted. When a note is discounted at a bank the payeeindorsesit, making it payable to the bank. Both maker and payee are then responsible to the bank for its payment. If the note is drawing interest the discount is reckoned on and deducted from the amount due at maturity. Most notes discounted at banks do not draw interest. Thetimein bank discount is always the number of days from the date of discounting to the date of maturity.
Example:A note of $250, dated July 7, payable in 60 days, is discounted July 7 at 6%; find the proceeds.
Explanation:This note is due in 63 days, or September 8. The accurate interest of $250 for 63 days at 6% is $2.59. The proceeds, then, will be $250-$2.59, or $247.41.
ThePresent Worthof a note or debt is a sum, which, if put at interest, will amount to that debt in the given time.
TheTrue Discountis the difference between the debt at maturity and its present worth.
Remember:
1.To allow three days of grace, if the debt discounted is a note.
2.To add the interest due at maturity to the principal, before discounting, if the note bears interest.
Examples:Case I.—Note not bearing interest.
What is the present worth and true discount on a note of $200, if paid 6 months before due, the discount being 6%.
Solution:Amount of $1 for 6 months at 6% = $1.03. If $1.03 = amount of $1, $200 is the amount of as many dollars as200⁄1.03, or $194.17+.
$194.17 is the present worth. $200 - $194.17 = $5.83 true discount.
The following rule can be deduced from the foregoing solution:—
Rule:1.To find the present worth, divide the debt by the amount of $1 for the given time.
2.To find the true discount, subtract the present worth from the debt.
Case II.—Note bearing interest.
What is the present worth of a note of $300, bearing 6% interest, due in 2 years 4 months, if money is worth 10%.
Solution:Interest on $300 for 2 years 4 months at 6% = $42.
$300 + $42 = $342. Amount due at maturity.
Amount of $1 for 2 years 4 months at 10% = $1.231⁄3.
If$1.231⁄3= amount of $1, then $3.42 is the amount of $3421.231⁄3, or $277.29.
$277.29 = present worth.
If a person borrows money, he usually pays something for the loan.
The sum of money he borrows is called thePrincipal; the money he pays for the use of the principal is calledInterest. Interest is generally reckoned at so much for the use of each $100 for one year. This amount is called theRate per cent per Annum.
Thus, if we say that $200 is borrowed for three years at 4 per cent per annum, we mean that the borrower, at the end of each year, pays the lender $4 for each $100 borrowed—i.e., $8 interest for each year.
In the above example the interest is supposed to be paid to the lender at the end of each year. Interest thus reckoned is calledSimple Interest.
The sum obtained by adding the interest for any given time to the principal is called theAmountin that time.
If we were to find the interest on a sum of money for 3 years 4 months 5 days, we would find the interest for 1 year, then for 1 month (1⁄12of a year), then for 1 day (1⁄360of a year). Having the interest for 1 year 1 month 1 day, it is a simple matter of multiplication to get it for 3 years 4 months 5 days.
Example:
What is the interest on $520 for 1 year 3 months at 6%?
In what is called the 60-Day Method, 360 days are considered one year, and 30 days one month. Upon this basis the interest for 60 days, or two months, at any rate, will be1⁄6of the interest for one year; and when the rate is 6% the interest for 60 days is one per cent or1⁄100of the principal. Thus, the interest of $247 for 60 days at 6% is $2.47.
Example: Find the interest of $1728 for 80 days at 6%.
Work:$1728= interest for 60 days.576= interest for 20 days.$2304= interest for 80 days.Explanation:The interest of $1728 for 60 days at 6% is 1% of $1728, or $17.28; and the interest for 20 days (1⁄3of 60) is1⁄3of $17.28, or $5.76. Hence for 80 days it will be $17.28 plus $5.76, or $23.04.
Work:$1728= interest for 60 days.576= interest for 20 days.$2304= interest for 80 days.
Work:
Explanation:
The interest of $1728 for 60 days at 6% is 1% of $1728, or $17.28; and the interest for 20 days (1⁄3of 60) is1⁄3of $17.28, or $5.76. Hence for 80 days it will be $17.28 plus $5.76, or $23.04.
The Common Method.—When the time is long, generally 30 days are considered a month.
The Exact Method.—When the time is short, the exact number of days is generally counted but we sometimes find the exact number of days also when the time is long.
The Bankers’ Method.—Bankers get the exact number of days between two dates, but each day is reckoned as1⁄360of a year.
Problem, when the time is long.
Find the time between April 12, 1895, and September 22, 1899.
Best Method
From April 12, 1895, to April 12, 1899, is 4years.From April 12, 1899, to Sept. 12, 1899, is 5months.From Sept. 12, 1899, to Sept. 22, 1899, is 10days.Time between dates = 4 years 5 months 10 days.
Another Method
Problem, when the time is short. Find the difference in time between April 12 and July 15, 1902.
Work:
Note.—If the rate and principal are given, it is a simple matter to find the interest, now that we have the time.
Example of the use ofTable: What is the time from February 10 to October 18, in the same year. February 10 is numbered 41, and October 18 is numbered 291; 291 - 41 = 250,Ans.This includes the last day, but not the first. If both days are taken, subtract 40 from 291 = 251,Ans.When February 29 occurs in a term, count an additional day. The day of the date of a note is not included in its term; thus, required the last day of grace of a note dated March 24, at 90 days. March 24 = 83; 83 + 93 = 176 = June 25,Ans.
TABLE OF TIME, IN DAYSThe following table gives the exact time, in days, between two dates.
Interest computed, at regular intervals, on the sum of the principal and any unpaid interest, is calledcompound interest. In other words, as soon as interest becomes due and is unpaid, it begins to draw interest at the same rate as the principal. Compound interest is generally paid on the deposits in savings banks and is used in calculating amortization and sinking funds.
Interest may be compounded quarterly, semi-annually, annually, or at the end of any other period agreed upon. In some States the collection of compound interest is not permitted.
Example: Find the amount and the compound interest of $1200 at 6% for two years, interest compounded semi-annually.
in commerce is a method of making payments in distant places, without the actual transmission of money, but by a Bill of Exchange calledDraft, which is a written request upon one person to pay a certain sum to another or to his order. The person who orders the money to be paid, is called theDrawer; the one who is directed to pay it, theDrawee, and the one to whom it is directed to be paid, thePayee.
DomesticorInland Exchangeis exchange between places in the same country:Foreign Exchange, between different countries.
If, for every little business transaction, money had to be sent from one business center to another, much needless inconvenience and expense would be incurred.
A man in Chicago owes a man in New York City a sum of money. He can send it to him in one of five ways:—
Suppose Mr. White of Chicago owes Mr. Brown of Boston $200 for groceries and Mr. Allen of Boston owes Mr. Warner of Chicago $200 for rent. Wouldn’t it save expense and trouble if Mr. White should go to Mr. Warner and Mr. Allen to Mr. Brown? Thereby two debts are cancelled by two city transactions and no money need be sent from one city to another.
This is all there is to Exchange, only in business life banks instead of individuals transact the business.
Only a small percentage of the money really passes from one city to another.
Exchange in the United States is carried on mostly by banks located in the large cities, which charge a small fee for transacting the business.
TABLE OF COMMERCIAL LAW IN THE STATES
Note.—In many of the States it is impossible to place a fixed amount on personal property exempt. In the table above these states have no amount given in the personal property column. Days of grace have been abolished in all states except the following: Arkansas, Mississippi, South Carolina and Texas.
If the drawee accepts the draft, he writes across the face of it “Accepted” with the date and his signature. This is called anAcceptance.
Once accepted, the draft becomes a note, with the same laws regulating it. If the draft is not accepted, it is not binding and we say that it has been “dishonored.”
A bill of exchange is entitled to days of grace, if it is payable in a State where grace is allowed, unless a particular day is named in the draft. In most States, no grace is allowed on sight drafts.