final module bm

Business mathematics Mr. Marlon B. FloresTrimex Institute of Science and Technology - 2009-

Lesson IPERCENTAGE

Philippine population has been growing steadily through the years

from about 27 million in 1960 to about 70 million in the year 2000.

PERCENTAGE

In business and in our daily lives, we often compare numbers.

We may, for example, compare our population growth last year with our

population growth this year. In this case we will be using the percentage

formula. Computations of simple and compound interests, discounts, taxes

commissions and production growth are also based on the percentage

formula.

Percentage problems contain three elements:

1. The base – to which the problem refer

2. The rate – the amount, degree, etc. of anything in relation to units

of something else: as, the rate interest, the rate growth, the rate of

pay per month, the foreign exchange rate, etc. The rate can be

expressed in percent, decimal or fraction of the base.

3. the percentage – refers to the actual quantity or number of items

represented by the rate. If the base is in peso units, the percentage

must also be expressed in pesos. The percentage is the number that

is related to the base by the rate.

Destiny is not a matter of chance, but it’s a matter of choice….1


In every problem where two of these factors are given, the third can be

found by means of this basic formula.

Where: P = Percentage

B = Base

R = Rate

Finding the percentage, we multiply base from the rate, as,

Example 1:

Our Gross National Product (GNP) last year (1979) was about P 89

billion. It is estimated that our GNP would grow by 6% next year (1980). By

how much would our GNP grow?

Solution:

Given: B = P 89 Billion

R = 6%

P = ?

P = B X R

P = P 89 billion X .06

P = P 5.34 Billion

Example 2:

During the last CPA examination, 18 percent of the 23, 000 examiners

passed the exams. How many passed the exams?

Solution:

Given: B = 23, 000 examiners

R = 18 %

P = ?

P = B X R

P =23, 000 X .18

P = 4, 140 examinees


P = B X R

P = B X R


Finding the Base

To find the Base, we modify the basic formula P =B X R, by

dividing both sides of the equation by R. This procedure will enable us to

find the answer for B.

P =B X R

B =PR

Example 1:

Usumaki Naruto pays P 310 a month for miscellaneous expenses.

After careful calculation, he computed that this was 10% of his monthly

salary. How much does Naruto earn each month?

Solution:

Given: P = P 310

R = 10%

B = ?

B =PR

B = P 3,100.00

Example 2:

Sasuke,s Restaurant desires a profit of P 56,000 which will be 14%

of its annual sales. How much it sell to realize this profit?

Solution:

Given: P = P 56, 000

R = 14%

B = ?

B = P

Destiny is not a matter of chance, but it’s a matter of choice….

B =P

310.10

3


R

B = P 400, 000

Check:

P = B X R

P = P 400, 000 X .14

P = P 56, 000

Finding the Rate

To find the rate, let us first convert the basic formula P = B X R

by dividing both sides of the equation by B. We know that dividing both

sides of the equation by B does not change the value of the equation.

P =B X R

Example 1:

Our Gross National Product in 1979 was valued at about

P 89 Billion in 1980, this value increased by P 5.34 billion. What was our

GNP growth rate?

Solution:

Given: P = P 56, 000

B = P 89 billion

R = ?


B =P 56, 000

.14

R =PB

4


R =PB

R = .06 or 6%

Example 2:

During the last CPA exams, 4, 140 out of 23, 000 examineees passed

the exams. How many percent passed the exam?

Solution:

Given: P = 4, 140 examinees

B = 23, 000

R = ?

R =PB

R = .18 or 18%

QUIZ NO ______

Name: ___________________________ Score _________________


R =P

5.34P 89

R =4, 140

23, 000

5


Course/Section: ___________________ Instructor: __________________

Exercise 3.1a

Find the percentage.

1. 30% of 80 6. 23% of 5,700 students

2. 75% of 78 7. 12 ½ % of 650 books

3. 19% of 89 8. 14% of P58,000

4. 145% of 95 9. 100% of $24,000

5. 200% of 360 10. 250% of P35 billion

Exercise 3.1b

Find the rate or the base.

1. 12 out of 48 stores 6. 5 is 10% of absences

2. 150 out of 2,000 examinees 7. 45 is 50% of attempts

3. 15 out of 20 games 8. 10 is 25% of production

4. P20 out of P100 sales 9. P6.50 is 2% of sales tax

5. P25 out of P150 profit 10. P1,500 is 20% of income

QUIZ NO ______Name: ___________________________ Score ____________________



Course/Section: ___________________ Instructor: __________________

PERCENTAGESolve the following problems.

1. Sixto’s shoes, Inc. Produced 34,500 pairs of shoes last year. Its capacity is 40,000 pairs of shoes. At what percent of capacity was Sixto operating last year?

2. Last season, the basketball team of a certain school played 22 games and won 14 of them. What percent of the games did the team win?

3. A raise of 15% brings P1, 200 a month to Nick Padilla’s salary. What was his salary a month?



4. Mr, Jun Umali pays P5, 000 a year as a tax of 3% of his lot in Marikina. How much is the assessed value of his lot?



5. Reputable Insurance Company Earned P7, 650, 000 this year. If its earning now are 20% more than last year’s, how much was the company’s earnings last year?

6. When Gary Garcia bought a bike, the sales representative asked for a deposit of 25% of the cost of bike. If he gave P250, what was the total cost of the bike?



7. A brand of Ela’s Clothing Company sells at P350 each, a gain of 18% over cost. Find (a) the cost of the product, and (b) the profit in pesos.

8. A company employs 250 people. If 25% are sales workers, 15% office workers, 10% administrative employees, and the rest production workers, how many employees are in each group?



9. Out of an income of P45,600 per year, Lydia Villano spent 48 1/3 % on food, 25% on rent, 10 ¾ on clothing, 8% on miscellaneous items, and the rest she saved.a) How much did she spend for each category?b) How much money did she save?

10. A caterer spent P5, 000 for a birthday party. 60% was for the ingredients of the food to be prepared, 305 was for the salaries of the waiters and 10% went to the fuel and ware handling. How much did the caterer spend for each item? If she charged 40% of the capital as her gain, how much was her profit?

Establishing Retail Prices



Lesson II

Markon, Markup and Markdown

People go into business because they have some goods to offer

the public for sale, or because they can render some services other people

need. In the process these businessmen make profits. Operating a retail store

successfully is not an easy thing to do. The retail store owner performs all

the basic functions of an enterprise – buying, financing, pricing, selling and

servicing. These functions are by no means easy and to many people who

lack entrepreneurial ability, running a retail store might prove a disaster.

Hundreds and thousands of businesses close shop every year because their

owners are not making profits.

A businessman has to worry about his sales. If he does not

have enough sales, then he is in big trouble. Among other things, a

successful retailer must know how to price his goods.

He must set prices high enough to cover different costs. First,

he must consider his operating costs. These include expenses like wages,

rentals, insurance, depreciation, light and water, and utilities. These costs are

called overhead costs.

Second, he must consider his selling costs. These include

expenses like freight charges, transportation expenses, tips, display, mail and

others.

And finally, he must consider the profit he must derive to

reward his efforts and risks and to keep his business going.

If a retailer sets too high prices, he might lose customers to

competitors. If his prices are too low, he may only ‘break-even” or even lose

many. Thus, pricing and selling products are important factors to consider in

managing a retail store, or any other business for that matter.

Markon



The difference between the selling prices of an article and the

cost of the article is called markon. For example, if Mrs. Sunade decides to

sell at P 90.00, the

T-shirts she bought for P 75.00, P 75.00 is the cost, P 90.00 is the selling

price; and P 15.00 is the markon .

Thus, we can say,

( Markon = Selling Price – Cost )

Markon Based on Cost

Many retailers, however, express markon as a percent or fraction of

the cost of goods to be sold. This markon varies from one store to another,

product to product. Thus, Mrs. Sunade may decide to apply a markon of

30% on clothes, or 35% on cosmetics, etc.

Example:

One line of women’s bra cost Mrs. Surayda P 50.00 each. At what

price should each dress be marked for sale if she wants to realize a 30%

markon based on the cost?

Solution:

Given: P 50.00 = cost of bra

30% = markon

1. Since the markon is 30% of the cost of P 50.00, the markon is computed

by multiplying P 50.00 by 30% . Thus,

Markon = Cost of Good X Markon Rate

= P 50.00 X .30

= P 15.00

2. The selling price is obtained by adding the markon to the cost of the

product.

Selling Price = Cost of Goods + Markon

= P 50.00 + 15.00

= P 65.00



We must realize, however, that the cost of the transportation, such as a

freight and trucking charges, and other operating expenses are part of the

cost of the product because these are considered essential parts of the costs

of the goods.

Markon based on the selling Price

We mentioned before that many retailers express markon as a percent

or as a fraction of the cost of goods to be sold. Other retailers, however,

prefer to state markon as a percent or fraction of selling price. What are the

differences of the practices? Let us illustrate by the following examples.

Excample 1:

An article costs P 40.00 and sells for P 55.00. Find the percent of

markon based on the selling price.

Solution:

Given: P 55.00 = selling price

P 40.00 = cost price

Markon = Selling Price - Cost Price

= P 55.00 – 40

= P 15.00

Markon Rate = Markon

Selling Price

Markon Rate = P 15.00

P 55.00

= 27.3 %

Excample 2:

Find the amount and the percent of markon based on the cost price if

an article costs P 20.00 and sells for p30.00.



Solution:

Given: P 30.00 = selling price

P 20.00 = cost price

Markon = Selling Price - Cost Price

= P 30.00 – P 20

= P 10.00

Markon Rate = Markon

Selling Price

Markon Rate = P 10.00

P 30.00

= 33.3 %

Markdown

Sometimes wholesalers or retailers reduce prices on various items in

their stores. Among the reasons given are: to attract more sales, to meet the

prices of competitors, to clear the store of old stocks or of merchandise that

is not selling well. Another way of clearing the stores of old stocks is to sell

at bargain prices during special occasions like Christmas sale, inventory

sale, clearance sale. The practice of reducing the regular selling price is

called a Markdown.

We can show how to compute for the markdown through the

following example.

Example 1:

Sharon Cuneta, a retail store owner offered for sale at P 110.00 for

goods that were originally priced at P 160.00. Find: (a) the markdown, and

(b) the percent of the markdown.

Solution:

1. To find the markdown, we have:

Markdown = P 160.00 – 110

= P 50.00


Markdown = Original selling price – New selling price


2. To find the markdown rate, we divide the amount of markdown by

the original selling price.

= 31.25%

Example 2:

Find the Markdown and markdown rate for a book which was

originally tagged at P 50.00, but is now being sold at P 35.00.

Solution

Markdown = P 50 – P 35

= P 15

= 31.25%

Markup

With the way prices change nowadays, it is not an uncommon

occurrence for retailers to raise their prices. From an original retail price , a

retailer may raise the regular selling price of his remaining stock because of

a prescribed increase in price. The amount by which the regular selling is

increased is called Markup.

The following examples will show how this term is being used.


Markdown = Original selling price – New selling price


Example 1:

A commodity originally tagged at P 32.70 is now being sold for

P 40.00. Find: (a) the markup, and (b) the markup rate.

Solution:

Given: P 32.70 - Previous Selling Price

P 40.00 - Increased selling Price

= P 40.00 – P 32.70

= P 7.30

= 22.3%

Sometimes retailers term previous selling price as regular selling price and

the increased selling price as new selling price.

Example 2:

Novo is increasing the selling price of belts from P 75.00 to P 90.00.

What is the percent of markup?

Solution:

Given: P 32.70 - Regular Selling Price

P 40.00 - New Selling Price

= P 90.00 – P 75.00

= P 15.00

= .20 or 20%

= 31.25


Markup = Increased Selling Price – Previous selling Price

Markup = New Selling Price – Regular Selling Price


Quiz no. _____

Name: __________________________ Rating: ___________________

Course & section: _________________ Instructor: __________________

Find the Markon and the selling Price for each of the following.



Quiz no. _____

Name: __________________________ Rating: ___________________


Find the amount and the percent of markon based on the selling price for each of the following:



Quiz no. _____

Name: __________________________ Rating: ___________________


Solve the following problems.

1. At what price should an office equipment sales representative sell portable

typewriters purchased at the cost of P 1, 985.00 and if the markon rate is

35%?

2. Good Fit Shoe Emporium bought children’s shoes at P 199.95 a pair. At

what price should the shoes be sold if the 30% markon rate on the cost is

imposed?



3. Yoshiharu purchased ballpens at a cost of P 42.00 a dozen. At what price

will he have to sell each ballpen in order to realize a 40% profit on cost?

4. Inuyasha purchased a lamp. The cost of the lamp was P 59.95, and the

shipping expense was P 1.50. How much must the selling price be, if a 28%

profit based on the cost is to be realized?



5. A retailer bought a dozen of pad paper costing P 72.00. At what price

must she sell if she wants to realize a 30% profit cost?

6. Temari, Inc. purchased typewriters worth P 2, 800 each. At what price

should the typewriters be sold if the 30% markon rate is based on the selling

price?



7. Gaara’s store purchased lampshades at P 720.00 each. At what price

should they be sold if the markopn rate is 33 ½% and is based on the selling

price?

8. Neji’s Bookstore purchased a dozen pencils costing P 36.00. At what

price should a pencil be sold if the markon rate is 35% based on the selling

price?



9. At what price should a sales representative sell calculators purchased at

P 450.00 each if the markon rate is 35% based on the selling price?

10. Shikamaru Shoes, Inc. bought men’s shoes at P 185.00 a pair. At what

price should the shoes be sold if a 33 ½ markon rate on the selling price is

imposed?



Quiz no. _____

Name: __________________________ Rating: ___________________


Find the markdown and the markdown rate for each of the following articles.

No.Original

PriceReduced

Price Markdown

MarkdownRate

1 P 65.00 P 50.00

2 120.00 95.00

3 29.95 19.95

4 20.00 15.50

5 45.00 34.95

6 215.50 194.95

7 340.00 270.00

8 79.95 65.50

9 520.00 479.95

10 839.95 750.00

11 37.50 29.95

12 146.60 99.95

13 679.90 610.00

14 489.95 425.50

15 99.95 85.50



Quiz no. _____

Name: __________________________ Rating: ___________________


Find the markup and the markup rate for each of the following article:

No.New Selling

Price

Regular SellingPrice

MarkupMarkup

Rate

1 P 30.25 25.00

2 51.95 45.00

3 28.90 24.95

4 17.00 15.50

5 160.00 149.95

6 235.00 200.00

7 86.90 80.00

8 179.95 150.00

9 48.85 45.50

10 346.60 310.00

11 550.00 499.95

12 178.85 149.95

13 98.80 81.50

14 650.00 599.95

15 150.00 139.95



Quiz no. _____

Name: __________________________ Rating: ___________________


Solve the following problems:

1. Notebooks that regularly sell for P 22.00 could be purchased for P 15.50

during a store’s clearance sale. What was the markdown rate?

2. A wristwatch that originally sold for P 350.00 is now priced at P 410.00.

Find the markon rate.



3. Kakashi’s bookstore sold a book that originally cost P 45.00 to P 30.00.

What are the markdown and the markdown rate?

4. At what price should be Optimus Prime sell screwdrivers purchased at

P 12.00 each if the markon rate is 25% based on the selling price?



5. Megatron bought one dozen of pad papers costing P 96.00. At what price

must he sell if he wants to realize a 30% profit on cost?

6. A markon of 35% based on the cost was added to the original cost of a

bed, which was sold for P 1, 300. What was the original cost?



7. An electric fan costs a retailer P 1, 800. He marks it on by 30%. Find the

selling price?

8. Ang’s Department Store operates on a markon of 40% of the cost. On this

basis, what is the selling price for shoes purchased at P 190.00 a pair?



9. G and Joe Company purchased a T-shirts at P 75.50and sold them at

P 89.95. At what percent of markon based on the selling price is the

company operating?

10. During a clearance sale, Hokage’s Department Store reduced the price of

its shirts from P 40.00 to P 29.95 each. What percent of markdown was the

consumer being offered?

DISCOUNT AND COMMISIONS



LESSON III

Introduction

Many consumers can get discounts if they buy in bulk or in big

numbers. The discount that they can get may range from 5% to 20% or even

higher. In our illustration, we notice that if the student buys only one book,

very often he would not get any discounts. But if he buys books not only for

himself but also for his classmates, the seller would be too willing to sell at

discount.

Terms to remember:

1. List price – the price at which an item is offered for sale to

the customer.

2. Discount – is an amount deducted from the list price. It is

often expressed as a certain percent of the list price.

3. Trade discount – are discounts given by manufacturers to

wholesalers, or by wholesalers to retailers.

4. Retail discount – are discounts given by the retailers to the

consumers.

5. Net price – is what the buyer actually pays for the goods. It is

the price obtained after deducting the discount from the list

price.

Trade discounts

Businessmen want to sell more in greater volumes and develop an

establish client or “suki”. They do this by offering trade discounts.

A Trade discounts is a reduction in price offered by one business to another

business. This discount is normally given by manufacturers to wholesalers,

or by wholesalers to retailer. Thus a book publisher offers a discount to retail

bookstores or other outlets because these stores are in the trade.

Computing single trade discounts



Problems in discounts, similar to our percentage problems involve the following elements:

1. The percentage, which is the amount of discount.

2. The rate, which is the percent or rate of discount.

3. The base, which is the amount on which the discount is computed.

Example

Beta Company manufactures cassettes. In its catalog, a national stereo

is priced at P2, 400, less a discount to the trade of 25%. What will Patricia’s

Music stereo have to pay for the cassettes?

Solution:

This problem involves two elements: the discount and the net price

1. Discount = List price x discount rate

= P2, 400 x .25

= P600

2. Net price = List Price - discount

=P2, 400 – 600

=P1, 800

Finding the Discount Rate

In our previous discussion, we explain how to get the discount in the

net price. Some wholesalers, however, may list only the list price and the net

price. In this case, the buyer may want to know the discount rate being

offered so that it can be compared with the rate being offered by the others

suppliers.

Here are some examples to solve the problems of this nature.

Example



Philip’s Sports Center ordered merchandise listed at P230. The

invoice received showed the net price as P195.50. Find the discount rate

offered Philip’s Sport Center.

Solution:

From our discount problem, we have,

If we want to get the discount rate, we have to divide both sides of the

equation by the list price, as,

Discounts List price X discount rate

List price List price

Discount rate

List price

OR

Discount

We can now get the answer to Example 1, thus,

Discount rate

Where discount = List price – Net price

= P230 – P195.50

= P34.50

List price = P230.00

Discount rate =

= .15 Or 15% Answer

Finding the list price


Discount = List price x discount

34

P34.50P230

List priceDiscount rate

Discount

List price


Thus far, we have discussed how to find the discount and the discount

rate. There is still one element in the discount formula which is not

accounted for-the list price. If we know the discount and the discount rate,

how do we find the list price?

The following example will show us how this is done.

Example

When Philip ordered merchandise from a friend, he was given a trade

discount of 15% and, thus, saved P34.50. What was the list price of the

merchandise?

Solution:

Again from our discount problem, we have,

If we want to get the list price, we have to divide both sides of the

equation by the discount rate, as

Discount List price X discount rate

Discount rate discount rate

From this equation, we can now get the answer to our example, thus,

Given: Discount = P35.50

Discount Rate = 15% Or .15

List price =?

List price =

= P34.50

.15

= P230 Answer

DISCOUNT SERIES


Discount rate

Discount = List price X Discount rate

List priceDiscount

Discount rate

Discount


Occasionally, a business offers a special trade discount in addition to

the one ordinarily given. Thus, a company might advertise that for the next

15 days, all articles are subject not only to the usual trade discount of 20%

but also to a discount rate of 10%. This practice of giving two or more trade

discounts on the same article is known as discount series. Let us look at the

illustration below.

One might wonder why some business firms offer discount series

instead of the more simple single trade discounts. The reasons are varied: to

reduce inventory, to promote a product line, or simply to attract more

customers.

We have to remember, however, that the discount series of 20% and

10% is not the same as 30%. The two successive rates of 20% and 10% are

less than the single rate of 30%. A discount series of 20% and 10% means

that a reduction of 20%is to be taken on the original list price and 10% is to

be taken on the balance that remains after the first discount is subtracted

from the list price.

Here is some example to illustrate how to compute for discount series.

Example


Announcing

Singer Beds – The Company for All Needs

On the luxurious “Mariposa Beds “Line

20 % AND 10%

SPECIAL DISCOUNTS


Nilda Sadorra purchased a typewriter at the list price of P2, 600, less

20% and 10%. How much must Nilda pay for the typewriter?

Solution:

1. First Discount = List price X First Discount rate= P2, 600 X .20= P520

2. First Balance = List price – First discount= P2, 600 – P520= P2, 080

3. Second Discount = First Balance X Second Discount Rate= P2, 080 X .10= P208

4. Net Price = First Balance – Second Discount= P2080 – P208= P1, 872

If Nilda purchased the same typewriter less 30%, how much should she pay?

Solution:

1. Discount = List price X Discount Rate= P2, 600 X .30= P780

2. Net Price = List price – Discount= P2, 600 – P780= P1, 820

Notice that the two successive rates of 20% and 10% are less than the single

rate of 30%. In the other words, Nilda would have paid less had she been

offered a single 30% discount instead of the discount series of 20% and

10%.

CASH DISCOUNTS



One of the big problems of business today is the collection of unpaid

accounts. With widespread use of credit, many buyers tend to overbuy. We

often hear of firms reprocessing some appliance sold ion credit simply

because of the inability of the buyer to pay. For many firms, it is a common

practice to provide contingencies for bad debts.

Thus, we see that it is important to seller to be paid by the buyer as

soon as possible. T o encourage prompt payment, the seller may offer a cash

discount of say 1, 2, 3, or 4%.

However, it is not always possible for buyers for pay in cash. There

are many reliable buyers who really pay given some terms to pay. Thus, the

seller may allow a specified lapse of time before he collects payment.

ARREARAGES

One of the big problems of business today is the collection of unpaid

accounts. With widespread use of credit, many buyers tend to overbuy. We

often hear of firms reprocessing some appliance sold ion credit simply

because of the inability of the buyer to pay. Even banks are not spared from

this problem.

Just recently, Central Bank Governor Gregorio Licaros mentioned that

the total arrearages of the entire banking system were still running high

despite corrective efforts introduced by the monetary authorities in the last

few years.

Speaking before the meeting of the bank administration institute,

Licaros disclosed that the out of the P70 billion outstanding domestic credits

as of June 30, 1979, aggregate arrearages amounted to P11.7 billion –an

amount he described as “disheartening”.

Pointing out that loans extended to delinquent borrowers prevent the

generation of incremental income and freeze a substantial portion of the



country’s financial resources, Licaros urged the bankers to exercise

discretion and sound judgment in extending to under take a study on the

causes of problem loans, both from the view point of the lender and the

borrower. “these studies,” he said, ”should lead suggestions for remedial

measures which the banks and the monetary authorities could adopt”

Terms of sale

The most common terms of sale as practiced by many business establishments are defined below.

C.O.D – Cash on delivery. Payment is given on the day the goods are delivered.

n/15,n/30,n/45 – Net due in 15,30, or 45 days. No cash discount is offered for prompt payment.

3/15,n/30 – A 3% cash discount is offered if the bill is paid within 15 days of the date of the invoice. If the discount term is not taken advantage of, the full amount must be paid within 30 days of the date of the invoice.

n/e.o.m – Net due at the end of the month. The bill must be paid by the last day of the month of the invoice.

n/15 e.o.m –Net due 15 days after the end of the month regardless of the date of the invoice.

2/15 e.o.m – Regardless of the date of the invoice, 2% maybe deducted if it is paid within 15 days after the end of the month.

n/15 r.o.g – Net due 15days after receipt of goods.To determine the due date, exact calendar days are counted. Here are

some tips to determine the exact calendar days.

1. When a sale is made after the 15th day of a month, for n/e.o.m. terms, postpone payment until the end of the following month. For example, an invoice day august 17 is due by September 30.

2. When a sale is made after the 26th of a month with terms n/15 e.o.m., payment is due by the 15th of the second month following. Thus, an invoice date august 28, is due by October 15.

Let us look at the following examples.

Example



A sale of sala sets costing P3, 700 is made on April 15, 1988 with

terms 3/15,n/30. Find the net amount to be paid on (a) April 12, 1979, (b)

April 30.

Solution

a) Since April 12, 1988 within 15 days of the date of the invoice, a 3% cash discount is given.Formula:

Cash discount = .03 X P3, 700 = P111

Net Amount to be paid = P3, 700 – P111 = P3, 589

b) April 30 is beyond the discount period. Thus, Net amount to be Paid = P3, 700.

Example 2.An invoice for P 830 is dated May 19, 1988. Find the amount to

be paid on (a) May 22, (b) June 6 (c) June 25 terms of sale are: 3/15 , 2/30,

n/45.

Solutions: (a) Since May 22, 1988 is within 15 days of the date of the invoice,

deduct 3% cash discount.Cash discount = P 830 x .03

= P 24.90

Net to be paid = P 830 – P 24.90 = P 805.10

(b) June 6, 1988 falls within 30 days of the date of the invoice, thus deduct 2% cash discount.

Cash discount = P 830 x .02 = P 16.60

Net amount to be paid = P 830 – P 16.60 = P 813.40



(c) June 25, 1988 falls within 45 days of the date of the invoice, thus no discount is given.

Net amount to be paid = P 830



QUIZ NO ______Name: ___________________________ Score _________________

Course/Section: ___________________ Instructor: _____________

Find the trade discount and the net price for each of the following purchases.



QUIZ NO ______Name: ___________________________ Score _________________

Course/Section: ___________________ Instructor: _____________

Find both the discount and the discount rate for each of the following purchases.

QUIZ NO ______



Name: ___________________________ Score _________________

Course/Section: ___________________ Instructor: _______________

Discounts and Commissions

Solve for the following problems

1. Usumaki Naruto’s Lighting Company purchased a dozen light bulbs for P

9.00 each. This purchased was subject to a trade discount of 25%. What was

the total net price?

2. Tandang Sunade’s Sporting Goods sold to one of its dealer’s a dozen

sports jackets at P 95.00 each and 2 dozens of sports pants at 120.00 each.

The entire purchased carried with it a discount rate of 20%. Find the total net

price to the dealer



3. One dealer in sports shirts offers a dozen at P 500.00 list price, less a 15%

discount. A second offers the same shirts for P 520.00 a dozen less a 20%

discount. Which is the better offer and by how much?

4. A dress was sold with a discount of P 25.93, which is 15% of the original

price. For how much did the dress sell?



5. A discount of P 120.00 for merchandise was given to a dealer after a trade

discount of 15 % on the list price. How much was the original price of the

merchandise

6. After deducting P 166.00 from the list price of a bill, P 664.00 was paid.

The discount was what percent of the list price?



7. After deducting P 81.20 from the list price of a Thermos , P 498.80 was

paid. The discount was what percent of the list price?

8. A table lamp was sold with a discount of P 35.16, which is 8 ¼ % of the

original price. What was the list price of the table lamp?



9. A pair of shoes sells for P 195.50 less 5%. What is the net price of the pair

of shoes?

10. A store is offering a dining table for P 1, 640vwith a discount of P 246.

The disclount was what percent of the list price?



QUIZ NO ______

Name: ___________________________ Score _________________

Course/Section: ___________________ Instructor: ______________

Find the Net Price of each purchase.



QUIZ NO ______

Name: ___________________________ Score _________________

Course/Section: ___________________ Instructor: _______________

Solve the following problems

1. The list price of a gas range is P 2, 100. If this price is subject to discounts

of 10% and 5%, what is the net price?

2. C and L Office Machines purchased five calculators listed at P 550.00

each, less 12% and 5%. How much did the calculators cost C and L Office

Machines?



3. Find the amount due on a merchandise listed at P 2, 080, less discounts of

14% and 6%.

4. A furniture dealer bought six table carts listed at P 520.00 each subject to

discount rates of 10% and 5%. If the freight cost was P 20.00, how much did

the table cost?



5. Which is more favorable to a buyer and by how much: 1,500 less

discounts of 15% and 5%, or a discount of 10% and 10%?

6. Which purchase is preferable: P 2, 100 dining table with discounts of 20%

and 10%, or a similar table with discounts of 15% and 15%?



7. Which offers the better discount: Store A with discounts of 15% and 10%

or store B with discounts of 12% and 15% ? The list price of the

merchandise is P 3, 250.



SIMPLE INTEREST COMPUTATIONLESSON 1

IntroductionIf you barrow a car from Avis or from any other car rental firms, or if you

live in some other person’s house or apartment, you are expected to pay for

the use of the car or for the use of the apartment. We call such payments

rent. Similarly, if you borrow money from someone or from institutions like

banks, you are expected to pay for the privilege. The payment for the use

money is called interest

Interest is the major source of income for banks. Three factors

determine how much interest is charged for a loan: the principal, the time

and the rate.

The principal is the number of pesos on which interest is calculated. It

is also referred to as the amount of the loan. The interest rate is the percent

of the principal to be paid each unit of time. The time or term is the number

of units expressed in days, months, or years for which the money is

borrowed. It also means the length of time given the borrower to repay the

loan.

The interest rate is expressed as a percent. A rate of 12%, for example,

means that the borrower must pay P12.00 for each P100.0 that he borrows

for period of one year. Time can also be expressed in years or a fraction of a

year such as half year, quarter year, five-twelfth year. If it is expressed in

days, weeks, or months, these are usually changed to equivalent fractions of

the year.

Formulas for Simple Interest

As we have just mentioned, the simple interest on a given principal at

a given time is the product of three factors: the principal, the rate of interest

and the number of units of time. The amount of interest paid for a loan may

be computed by using the simple interest formula:



Where:

I = the amount of the interest

P= principal (the amount of money borrowed)

r = the rate at which the interest is to paid

t = length of time the debt has to be paid

If went to find out the total amount of pesos a person earns at the end of n

years, we have:

A = P + I

Where:

P = the principal

I = the amount of interest

A = the total amount of pesos earned

The formula can still further refined into:

A = P + I

I = prt

A = P + prt = P (1 + rt)

Problem 1:

What is the simple interest on P4, 000 for 2 years of 6%? What is the

amount?

Solution:

Here we have: P = P4, 000

r = .06 (6%)

t = 2

I = prt

= P4, 000 x .06 x 2

I = P480 (Interest)

And


I = prt


A = P + I

= P4, 000 + 480

= P4, 480 (Amount)

Or

A = P(1 = rt)

= 4, 000(1 = [.06 x 2])

= 4,000 (1 + .12)

= 4, 000(1.12)

= P4, 480 (Amount)

Problem 2

Find the interest and the amount for P800 for 8 months at 4%.

Solution:

Here we have: P = 800

r = 4/100 (4%)

t = 8/12 (8 months in one year)

I = prt

= 800 x 4/100 x 8/12

I = 64/3

And

A = P + I

= P800 + 21.33

A = P821.33 (Amount)



Derived Interest Formula

So far, we have just been looking for the interest while the variables

of the principal, rate, and time are given. Thus, we are familiar with the

formula:

With our knowledge of the properties of an equation, we can see the

possibility of deriving three other equations. These derivations can be made

possible by applying the Axiom of Division.

1. Finding the Principal

Lenders frequently ask how much principal will be

required to produce a given amount with the interest, rate,

and time given. The following derivation can help us solve

this problem.

Problem 3:

At the end of 10 months, the amount of P160.00 was paid as interest

at 6%. How much was borrowed?

Given:

I = P160

r = 6% (6/100)

t = 10/12 = 5/6


I = prt

I = prt

P = I / rt


Solution

=

=

=

=

2. Finding the Rate

Given the principal, interest, and time, we can determine the

rate necessary to produce a given yield. The following formula is

used.

Problem 4

At what rate in simple interest must I invest my P1, 200 in order to

earn an interest of P60 for 8 months?

Given:

I = P60

P = 1, 200

t = 8/12 = 2/3


160

11

160

6 5

100 6

1

20

20 1

160 X1

20

P3, 200 (Principal)P

P

I = prt

P = I / pt

I

rt


Solution:

=

=

=

=

3. Finding the Time

Given the principal, interest, and time, we can determine the

rate necessary to produce a given yield. The following formula is

used.

Problem 5:

Find the time necessary to yield P30.00 on P450 at 8% simple interest.

Given:

P = P450

I = P30

R = 8%

t =?


rI

pt

60

800

1, 2000

3

2

1

400

X

60

r .075 Or 7.5% (rate)

I = prt

P = I / pr


Solution:

=

=

=

=

=


t I

pr

36

30

4.5

30

30

1

450

100

84.5

X

X 8

6

5

Year or 10 months 6

5( = 10 months. )X

1

12

2

1

t


TRIMEX COMPUTER SCHOOL

Name: _________________________Rating: ____________________

Course & section: ________________Instructor: _________________

Exercise 1

1. Find the simple interest and amount of (a) P1, 500 for 2 years

at 5%, (b) 2,050 for 9 months at 6%?

2. Find the simple interest and amount of (a) P3, 800 for 10

months at 10 ½ % (b.) P4, 100 for 1 ½ years of 6 ¾%.

3. Find the interest on the amount of:

a) P600 for 1 year of 5%

b) P600 for 6 months at 5%

c) P600 for 3 months at5%

d) P1, 400 for 1 year at 6 ½%

e) P1, 400 for 4 months at 6 ½%

f) P750 for 1 year at 8%

g) P750 for 6 months at 8 ½%

h) P3, 400 for 2 months at 6%

i) P3, 400 for 8 months at 6%

j) P5, 800 for 1 year at 7 2/3%

4. Find the interest on and the amount of:

a) P5, 300 for 1 year at 5 ½%

b) P5, 300 for 6 months at 5 1/3%

c) P5, 300 for 8 months at 6 ¼%

d) P6, 400 for 1 year at 6%

e) P6, 400 for 7 months at 6 ½%

f) P6, 400 for 10 months at 7 ½%

g) P780 for 1 year at 9%

h) P780 for 3 months at 10%

i) P780 for 8 months at 6%

j) P780 for 6 months at 7%



Exercise 2

1. Determine the ordinary interest of P540 from January 16 to

august 20 at 5%.

2. Find the interest of P5, 400 at 6% for 120 days.

3. How much interest would P6, 500 earn at 7% for 10 months?

4. Determine the interest of P6, 500 at 8% for 180 days.



5. Find the interest of P1, 800 at 10% for 9 months.

6. How much interest would P1, 800 earn at 8% for 210 days?

7. Determine the interest of P2, 400 from March 12 to July 25 at 6

½ %.

8. Find the interest of P2, 400 at 10% for 2 years.



9. How much interest would P4, 200 earn at 8% for 280 days?

10. Find the interest of P4, 200 at 6% for 8 months.


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