Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges

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114 Part 2 Percentage Applications

THE BOTTOM LINE

Summary of chapter learning objectives:

Learning Objective

6.1

Compute sales commissions and gross pay.

Example

1. A salesperson gets a $1,750 salary and a 2.5% commission. Find the

commission and the gross pay when sales are $58,400 and returns are

$6,800.

Answers: 1. Commission: $1,290; Gross pay: $3,040 2. $4,375 3. Commission: $546; Net proceeds: $14,635

4. Commission: $672; Gross cost: $9,286

6.2

Compute graduated sales commissions.

6.3

Compute sales and purchases for principals.

2. A salesperson has a graduated commission rate: 1% on sales up to

$100,000; 2% on sales from $100,000 to $200,000; and 2.5% on

sales above $200,000. Find the commission when sales are $255,000.

3. A broker sells a principal’s merchandise at a gross sales price of

$15,600 at a commission rate of 3.5%. There are sales costs of $300

for storage and $119 for delivery. Find the commission and net

proceeds.

4. A commission merchant purchases merchandise for a principal at a

prime cost of $8,400. The commission rate is 8%, air freight is $139,

and local delivery is $75. Find the commission and gross cost.

Chapter 6 Commissions 115

SELF-CHECK

Review Problems for Chapter 6

In problems 1–4, compute both the commission and the total pay based on the information given.

1 Salary, $3,000; commission rate, 6%; total sales, $58,000; returns, $0

a. Commission b. Total pay

2 Salary, $2,500; commission rate, 5%; total sales, $91,000; returns, $5,000

a. Commission b. Total pay

3 Salary, $3,600; commission rate, 4.5%; total sales, $76,000; returns, $6,800

a. Commission b. Total pay

4 Salary, $0; commission rate, 8%; total sales, $98,000; returns, $11,425

a. Commission b. Total pay

5 Compute the total commission on sales of $160,000 if the commission rates are 3% on the first $100,000 and 5%

on everything above $100,000.

6 Compute the total commission on sales of $85,000 if the commission rates are 3% on the first $100,000 and 5% on

everything above $100,000.

7 Compute the total commission on sales of $250,000 if the commission rates are 2% on the first $75,000; then 3%

on the next $75,000; and 4% on everything above $150,000.

8 Compute the total commission on sales of $135,000 if the commission rates are 2% on the first $75,000; then 3%

on the next $75,000; and 4% on everything above $150,000.

9 Compute the total commission on sales of $70,000 if the commission rates are 2% on the first $75,000; then 3% on

the next $75,000; and 4% on everything above $150,000.

10 Compute the total commission on sales of $115,000 if the commission rates are 4% on the first $35,000; then 6%

on the next $45,000; and 8% on everything above $80,000.

11 Larry Leong is paid 2.5% on all sales. He is also paid a bonus of an additional 1.5% on any sales above $70,000.

Calculate Larry’s total commission on sales of $120,000.

12 Gloria Alvares is paid 4% on all sales. She is also paid a bonus of an additional 2% on any sales above $40,000.

Calculate Gloria’s total commission on sales of $105,000.

13 Charles White sells used logging equipment on consignment. He charges 20% commission plus expenses. Calcu-

late Charles’s commission on a log truck he sold for $42,750.

14 For the sale in problem 13, Charles also paid an additional $290 to deliver the truck to the new owner. Calculate the

net proceeds that Charles’s principal should receive.

15 Sue Lyon is a designer who purchases furniture for clients. She charges 15% of the price, plus expenses. Calculate

Sue’s commission on furniture priced at $21,400.

16 For the sale in problem 15, calculate the gross cost to the client if Sue also had expenses of $646.

Answers to the Self-Check can be found in Appendix B at the back of the text.

116 Part 2 Percentage Applications

Notes

Chapter 6 Commissions 117

Assignment 6.1: Commission

Name

Date Score

A (24 points) Find the commission and the total gross pay. (2 points for each correct answer)

Monthly Commission Monthly Gross

Employee Salary Rate Sales Commission Pay

1. Li, Walter $ 0 8% $45,000

2. Starr, Karen 2,000 3% 36,000

3. Aguire, Luis 1,500 5% 42,000

4. Wallace, Fran 2,650 2.5% 58,000

5. Rogerro, George 1,800 6% 64,000

6. Tang, Suzanne 2,500 4% 57,000

Score for A (24)

B (36 points) Compute the total commission for the following commission payment plans. (6 points for each

correct answer)

Graduated Commission Rates Sales Commission

7. 2% on sales to $60,000 $106,000

4% on sales above $60,000

8. 1% on sales to $150,000 $188,000

2% on sales above $150,000

9. 3% on sales to $50,000 $ 94,400

5% on sales above $50,000

10. 1% on sales to $75,000 $240,000

2% on sales from $75,000 to $150,000

3% on sales above $150,000

11. 3% on sales to $50,000 $128,000

4% on sales from $50,000 to $100,000

5% on sales above $100,000

4,900

4,950

3,720

2,260

$3,040

0.04 3 $57,000 5 $2,280 1 $2,500 5 $4,780

4,7802,280

0.06 3 $64,000 5 $3,840 1 $1,800 5 $5,640

5,6403,840

0.025 3 $58,000 5 $1,450 1 $2,650 5 $4,100

4,1001,450

0.05 3 $42,000 5 $2,100 1 $1,500 5 $3,600

3,6002,100

0.03 3 $36,000 5 $1,080 1 $2,000 5 $3,080

3,0801,080

0.08 3 $45,000 5 $3,600 1 0 5 $3,600

$3,600$3,600

Learning Objectives

2 3

0.02 3 $60,000 5 $1,200

0.04 3 46,000 5 

1,840

$3,040

0.01 3 $150,000 5 $1,500

0.02 3 38,000 5 0

760

$2,260

0.03 3 $50,000 5 $1,500

0.05 3 44,400 5 

2,220

$3,720

0.01 3 $75,000 5 $ 750

0.02 3 75,000 5 1,500

0.03 3 90,000 5 

2,700

$4,950

0.03 3 $50,000 5 $1,500

0.04 3 50,000 5 2,000

0.05 3 28,000 5 

1,400

$4,900

12. 2% on sales to $65,000 $124,800

3% on sales from $65,000 to $130,000

4% on sales above $130,000

3,094

118 Part 2 Percentage Applications

Assignment 6.1 Continued

Score for B (36)

C (20 points) Janet Cronin is a commission merchant. She charges different commission rates to sell differ-

ent types of merchandise. During May, she completed the following consignment sales for consignors.

Find Janet’s commission on each sale and the net proceeds sent to each consignor. (2 points for each

correct answer)

Gross Comm. Local Air Net

Sales Rate Commission Delivery Storage Freight Proceeds

13. $38,400 3% $ 68 $ 0 $183

14. $1,600 4.5% 88 65 0

15. $8,400 6% 284 0 0

16. $12,880 5% 0 0 148

17. $14,100 7% 75 85 112

Score for C (20)

D (20 points) Alvin Guiterez, a commission merchant in Dallas, buys merchandise exclusively for

principals. Listed below are five recent transactions. Compute Alvin’s commission on each purchase

and the gross cost. (2 points for each correct answer)

Prime Comm. Local AirGross

Cost Rate Commission Delivery Storage Freight Cost

18. $16,600 5% $89 $ 88 $ 0

19. $4,900 11% 0 0 195

20. $8,400 6% 30 58 196

21. $4,850 8% 0 110 108

22. $26,450 10% 50 0 246

Score for D (20)

$26,450 3 0.10 $26,450 1 $2,645 1 $50 1 $246

$29,391$2,645

$4,850 3 0.08 $4,850 1 $388 1 $110 1 $108

$5,456$388

$8,400 3 0.06 $8,400 1 $504 1 $30 1 $58 1 $196

$9,188$504

$4,900 3 0.11 $4,900 1 $539 1 $195

$5,634$539

$16,600 3 0.05 $16,600 1 $830 1 $89 1 $88

$17,607$830

$14,100 3 0.07 $14,100 2 $987 2 $75 2 $85 2 $112

$12,841$987

$12,880 3 0.05 $12,880 2 $644 2 $148

$12,088$644

$8,400 3 0.06 $8,400 2 $504 2 $284

$7,612$504

$1,600 3 0.045 $1,600 2 $72 2 $88 2 $65

$1,375$72

$38,400 3 0.03 $38,400 2 $1,152 2 $68 2 $183

$36,997$1,152

0.02 3 $65,000 5 $1,300

0.03 3 59,800 51

1,794

$3,094

Chapter 6 Commissions 119

Assignment 6.2: Applications with Commission

Name

Date Score

A (56 points) Solve each of the following business application problems involving salespeople who are

paid partly or entirely on a commission basis. Solve the problems in order, because some of the ques-

tions are sequential. (8 points for each correct answer)

1. Pat Endicot sells memberships to an athletic club. He receives a monthly salary of $2,150 plus a

commission of 15% on new membership fees. What was Pat’s monthly pay for May, when he sold

new memberships valued at $27,500?

$6,275

Learning Objectives

2 3

2. Roberta Reavis sells commercial restaurant supplies and equipment. She is paid on a commission-only

basis. She receives 2% for her sales up to $60,000. For the next $90,000 of sales, she is paid 3%, and for

any sales above $150,000 she is paid 4%. How much commission would Roberta earn in a month when

her sales were $175,000?

$4,900

3. Roberta Reavis (problem 2) is not paid commission on any restaurant supplies or equipment that are later

returned. If an item is returned, its price is deducted from Roberta’s total sales to get her net sales. The com-

mission-only rate is applied to her net sales. Suppose that Roberta sold merchandise worth $175,000 but

that $40,000 of that was later returned. What would be Roberta’s commission on net sales?

$3,450

4. Dana Kline works for Southwest Appliance Depot. She receives a monthly salary of $2,500 for which she

must sell $20,000 worth of appliances. She also receives a commission of 4% on net sales above $20,000.

What will be Dana’s pay for October, when her net appliance sales were $42,000?

$3,380

5. Southwest Appliance Depot (problem 4) offers service contracts with all appliance sales. To encourage

salespeople such as Dana to sell more service contracts, the company pays a commission of 20% on all

service contracts. What will be her total pay for a month if she sells $42,000 worth of appliances and

$1,500 worth of service contracts?

$3,680

6. Stockbrokers for many investment firms are paid a commission on the stocks that they buy and sell for their

clients. Suppose that the commission rate is 0.5% of the value of the stock. What will the commission be on

5,000 shares of General Motors stock that is selling for $67.31 per share?

$1,682.75

5,000 3 $67.31 5 $336,550 0.005 3 $336,550 5 $1,682.75 commission

0.20 3 $ 1,500 5 $ 300 commission on service contracts

0.04 3 $22,000 5 880 commission on appliances

2,500 salary

$ 3,680 total pay

$42,000 net sales 0.04 3 $22,000 5 $ 880 commission

20,000 12,500 salary

$22,000 commission sales $3,380 monthly pay

$175,000 total sales 0.02 3 $60,000 5 $1,200

40,000 returns 0.03 3 75,000 512,250

$135,000 net sales $3,450 commission

0.02 3 $60,000 5 $1,200

0.03 3 90,000 5 2,700

0.04 3 25,000 51

1,000

$4,900 commission

0.15 3 $27,500 5 $4,125 commission

2,150 salary

$6,275 monthly pay

7. Michelle Sosa works in telemarketing. Her job is to make telephone calls from a computerized list of names

and try to convince people to make an appointment with a life insurance salesperson. Michelle receives 40¢

for each completed telephone call, $7.00 for each appointment made and kept, and 1% of any initial revenue

that results from the appointment. How much would Michelle earn if she completed 968 calls, 153 persons

made and kept appointments, and $37,600 in revenue resulted from the appointments?

$1,834.20

120 Part 2 Percentage Applications

Assignment 6.2 Continued

Score for A (56)

B (24 points) Solve each of the following business applications about consignment sales and commission

merchants. (8 points for each correct answer)

8. Theresa Fowler is a commission merchant who charges a 15% commission to sell antique furniture from

her showroom. Henry Marshal owns antique furniture, which he transports to her showroom where

Theresa sells it for $9,600. Henry agrees to pay Theresa $488 to have the furniture delivered to the buyer

from the showroom. What will be Henry’s net proceeds from the sale?

$7,672

9. Suppose, in problem 8, that payment of the $488 delivery expense was Theresa’s responsibility instead of

Henry’s. Then what would be Theresa’s net earnings from the sale?

$952

968 3 $0.40 5 $ 387.20 telephone calls

153 3 $7.00 5 1,071.00 appointments

0.01 3 $37,600 51

376.00 revenue percentage

$1,834.20 total earnings

Commission: $10,800 $180,000

Fees 1

3,500 2 14,300

Total costs: $14,300 $165,700 net proceeds

Commission: 0.06 3 $180,000 5 $10,800

Booth fees: 4 3 $500 5 $2,000 $32,400

Transportation: 425 2

8,905

Commission: 0.20 3 $32,400 516,480 $23,495

Total costs: $8,905

Commission: 0.15 3 $9,600 5 $1,440

Less delivery expense: 0

2488

$ 952

Commission: 0.15 3 $9,600 5 $1,440

Net proceeds: $9,600 2 $1,440 2 $488 5 $7,672

10. Sandy McCulloch makes artistic weavings that are used as wall hangings. She sells her weavings primarily

at open-air art shows and street fairs through her agent, Ruth Danielson. Ruth charges 20% on all sales,

plus the fees to operate the sales booths and transportation expenses. After selling at four art shows, Ruth

had total sales of $32,400. Each art show charged a booth fee of $500, and Ruth’s total transportation ex-

penses were $425. What were Sandy’s net proceeds?

$23,495

Score for B (24)

C (20 points) The following problems involve the purchase of a home. (10 points for each correct answer)

11. JoAnn Ednie has a condominium that she would like to sell and she asks real estate broker Gene Jenkins

to sell it. Gene, co-owner of Jenkins/Weekly Real Estate, advises JoAnn that she should be able to sell her

condominium for $180,000 and the commission rate for selling it will be 6%. If the condominium sells

for the expected price, what will be the total commission amount that JoAnn pays?

$10,800

12. See problem 11. To sell her condominium, JoAnn Ednie must also pay some additional fees for inspec-

tions, title insurance, and to record the sale. These fees total $3,500 and are added to the 6% commission.

What will JoAnn’s net proceeds be from the sale of her $180,000 condominium?

$165,700

Score for C (20)

Discounts

Chapter 7 Discounts 121

Learning Objectives

By studying this chapter and completing all assignments, you will be able to:

Compute trade discounts.

Compute a series of trade discounts.

Compute the equivalent single discount rate for a series of trade

discounts.

Compute cash discounts and remittance amounts for fully paid

invoices.

Compute cash discounts and remittance amounts for partially paid

invoices.

Learning Objective

Businesses that sell products want to attract and keep customers who make repeated,

large-volume, more expensive purchases. Manufacturers, distributors, and wholesalers

frequently offer trade discounts to buyers “in the trade,” generally based on the volume

purchased. For example, Eastern Restaurant Supply gives a 40% discount to Regal Meals,

a local chain of 34 sidewalk sandwich carts that sell hot dogs and sausage sandwiches.

Another Eastern customer is Suzi Wilson, founder and owner of Suzi’s Muffins. Suzi’s

business is still small. She bakes her muffins between 11

P.M. and 2 A.M. in oven space that

she leases from a bakery. Eastern gives Suzi only a 25% discount because she doesn’t do as

much business with Eastern as Regal Meals does. Eastern also sells to people who are not

“in the trade.” These retail customers pay the regular list price, or full price without any

discount.

Large restaurant chains such as McDonald’s and Burger King can go directly to the

manufacturer for most items or even do their own manufacturing. They can have items

manufactured to their exact specifications for a contracted price. They reduce their costs

by eliminating the distributors (the “middle men”).

The two traditional methods for computing trade discounts are the discount

method and the complement method. You can use both methods to find the net price

that a distributor will charge the customer after the discount. The discount method is

useful when you want to know both the net price and the actual amount of the trade

discount. The complement method is used to find only the net price. It gets its name

because you use the complement rate, which is 100% minus the discount rate. Each

method has only two steps.

When one business sells merchandise to another business, the seller often offers two

types of discounts: trade discounts and cash discounts. Trade discounts affect the agreed-

upon selling price before the sale happens. Cash discounts affect the amount actually

paid after the transaction.

122 Part 2 Percentage Applications

Computing Trade Discounts

Learning Objective

Compute trade discounts.

7.1 Students may be more familiar

with cash discounts than with trade

discounts.Trade discounts are dis-

cussed first because the trade discount

is awarded by the seller before the sale,

to encourage the sale,whereas the

cash discount is awarded after the sale,

to encourage the payment.

7.2 Ask students if either discount

method might be more useful to busi-

nesses.If the buyer is comparing differ-

ent sellers,what really should interest

the buyer is the ultimate net price.It

doesn’t make financial sense to base

the decision on a “larger discount”if

the net price isn’t lower.Compare the

situation to that of retailers that have

“big sales”at various times throughout

the year.Some retailers that have repu-

tations for large discounts also have

high original prices.

to Compute Net Price with the Discount Method

1. Multiply the discount rate by the list price to get the discount amount:

Discount 5 Trade discount rate 3 List price

2. Subtract the discount from the list price to get the net price:

Net price 5 List price 2 Discount

STEPS

EXAMPLE A

Eastern Restaurant Supply sells a set of stainless steel trays to Suzi’s Muffins. The list

price is $120, and Suzi qualifies for a 25% trade discount. Compute the net price using

the discount method.

Discount 5 0.25 3 $120 5 $30

Net price 5 $120 2 $30 5 $90

STEP 2

STEP 1

A distributor or manufacturer may give additional discounts to customers who actually

buy larger volumes. Suppose that Eastern Restaurant Supply gives all food preparation

businesses a 25% discount for being in the trade. However, if one business buys twice as

much from Eastern, it may be rewarded with additional discounts. For example, Suzi’s

Muffins may receive its first discount of 25% automatically. Then, Suzi’s gets an addi-

tional 20% discount if its accumulated purchases were between $10,000 and $25,000

during the previous year and another 10% if accumulated purchases were more than

$25,000 during the previous year. Therefore, Suzi’s Muffins could have discounts of 25%,

20%, and 10%, called a series of discounts.

Both the discount method and the complement method can be used to compute the

net price for a series of discounts. The two methods are the same as shown previously, ex-

cept that the steps are repeated for each discount in the series. For example, if there are

three discounts, repeat the steps three times. Apply the first discount rate to the list

price. For the second and third discounts, compute intermediate prices and then apply

the discount rates to them.

Chapter 7 Discounts 123

to Compute Net Price with the Complement Method

1. Subtract the discount rate from 100% to get the complement rate:

Complement rate 5 100% 2 Trade discount rate

2. Multiply the complement rate by the list price to get the net price:

Net price 5 Complement rate 3 List price

STEPS

EXAMPLE B

Using the data in example A, compute the net price, using the complement method.

Complement rate 5 100% 2 25% 5 75%

Net price 5 0.75 3 $120 5 $90

STEP 2

STEP 1

a. Compute the trade discount amount and

the net price, using the discount method.

List price 5 $240 Trade discount 5 30%

Discount amount 5 0.30 3 $240 5 $72

Net price 5 $240 2 $72 5 $168

b. Compute the complement rate and the net

price, using the complement method.

List price 5 $240 Trade discount 5 30%

Complement rate 5 100% 2 30% 5 70%

Net price 5 0.70 3 $240 5 $168

✔

CONCEPT CHECK 7.1

Compute a series of trade discounts.

Learning Objective

Computing a Series of Trade Discounts