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

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Please observe: In example H, Rueben will keep $49,250 for the entire 60 days and

then repay a total of $50,000 on the due date.

As mentioned earlier, some persons refer to this type of discounted loan as “non-

interest-bearing” because the amount to be repaid is the “face value.” However, the term

non-interest-bearing is misleading because the loan is not “interest-free.” There is a charge

of $750 to borrow $49,250 for 60 days.

COMPARING A DISCOUNT RATE TO AN

INTEREST RATE

Discount rates are less familiar to those consumers who have encountered only interest

rates. There is the possibility of misunderstanding or confusion. In example G, Rueben

Cortez borrowed $50,000 for 60 days and paid $750. The ordinary simple interest rate

was 9%. In example H, Rueben borrowed $49,250 for 60 days and paid $750. Although a

discount rate (9%) was given, a simple interest rate was not given. To compute Rueben’s

actual simple interest rate in example H, use the formula from Chapter 13:

R 5 , letting I 5 $750, P 5 $49,250, and T 5

R 55 5 50.09137, or 9.14%

The interest rate in example H is actually 9.14%; the discount rate is 9%. They are

different rates, but both lead to a $750 fee to borrow $49,250 for 60 days. A borrower

must understand the difference between interest rates and discount rates and how each

is used in loan calculations.

$750

$8,208.33

$750

$49,250 3

360

P 3 T

360

P 3 T

304 Part 4 Interest Applications

A bank made a 90-day loan on a discount basis.The face value was $64,000, and the discount

rate was 11%. Compute the discount amount and the proceeds.Then compute the actual

interest rate, using the proceeds as the principal of the loan instead of the face value. Use

a 360-day year in all calculations.

Discount amount 5 FV 3 R 3 T 5 $64,000 3 0.11 35$1,760

Proceeds 5 Face value 2 Discount amount 5 $64,000 2 $1,760 5 $62,240

Actual interest rate 55 50.1131, or 11.31%

$1,760

a$62,240 3

360

(P 3 T)

360

✔

CONCEPT CHECK 15.5

In Chapter 7, we described how manufacturers and wholesalers use cash discounts to

encourage their customers to pay their invoices early. Recall that the terms “2/10, net 30”

mean that the buyer will receive a 2% discount by paying the invoice within 10 days and

that the entire invoice is due within 30 days. However, it would be normal that a buyer

would not have the immediate cash to pay the invoice early. The buyer may need to sell

the merchandise to get the cash to pay the invoice. Normally, a buyer can save money by

borrowing money to pay the invoice early and earn the cash discount.

Chapter 15 Promissory Notes and Discounting 305

Borrowing Money to Take a Cash Discount

Compute the savings from

borrowing money to take a cash

discount.

Learning Objective

EXAMPLE I

DVD Central purchased $100,000 worth of CDs and DVDs. The invoice was dated October 4

with terms of 2/10, net 30. Compute the due date, the (cash) discount date, the cash discount,

and the total remittance required to get the cash discount. (Review Chapter 7 if necessary.

Notice that the terms “discount date” and “due date” had different meanings in Chapter 7 than

they have had here in Chapter 15.)

Due date 5 October 4 1 30 days 5 November 3

Discount date 5 October 4 1 10 days 5 October 14

If paid by October 14:

Cash discount 5 $100,000 3 0.02 5 $2,000

Total remittance 5 $100,000 2 $2,000 5 $98,000

Regardless of whether it takes the discount, DVD Central needs to pay $100,000 by

November 3. The company may want to save the $2,000, but perhaps it doesn’t have the

$98,000 now. Or maybe it has the money but wants to spend it on something else. In

either situation, DVD Central might be able to borrow the money from October 14 until

November 3. Before borrowing, DVD Central should compare the savings from the cash

discount with the interest on a loan.

15.4 As a review of Chapter 13,you or

the students could calculate what

interest rate on $98,000 for 20 days is

required to earn $2,000 interest.The

answer is 37.24%.This is the rate for

any purchase with terms of 2/10, net

30.By not taking the discount,the

buyer is missing the opportunity to

make a 37.24% investment.

EXAMPLE J

DVD Central can borrow $98,000 for 20 days (October 14 to November 3) by paying

10% exact simple interest (365-day year). Compute the interest on the loan and the

savings for DVD Central if it borrows to take the cash discount.

Interest 5 P 3 R 3 T 5 $98,000 3 0.10 35$536.99

Savings 5 $2,000 cash discount 2 $536.99 interest 5 $1,463.01

365

The reason for borrowing only between the (cash) discount date and the due date is

to delay making payments as long as possible, whether to get cash discounts or to avoid

penalties. The (cash) discount date is the latest possible date to pay and get the cash

discount; the due date is the latest possible date to pay and avoid a penalty.

Although borrowing and taking the cash discount is almost always cheaper, the actual

dollar amount may determine what DVD Central decides. If the original purchase were

only $1,000, the savings would be only $14.63. Such an amount may not be worth the

effort of getting a loan. However, for borrowing small amounts regularly, businesses

often have “revolving lines of credit.” These allow them to borrow and repay frequently,

without always making a new loan application.

15.5 The decision as to whether to pay

an invoice early or prolong payment for

as long as possible will also depend on

how strictly the seller enforces the late

payment penalty.When the buyer is

very large compared to the seller,the

seller may permit late payments just to

get and keep the business.In such

cases,the buyer may prefer to delay

payment for a long time at no penalty

instead of taking the discount.

306 Part 4 Interest Applications

A retailer purchases merchandise under the terms 1.5/20,net 45.The invoice is for $45,000

and is dated July 22. For the cash discount, calculate the due date, the (cash) discount date,

the amount of the cash discount, and the total remittance required.The retailer borrows

enough money to pay the entire remittance.The interest rate is 12% exact simple interest,

and the loan is for the length of time between the last date to take advantage of the cash

discount and the due date. Calculate the amount of the interest and the savings gained by

borrowing the remittance to take the discount.

Discount: Due date: July 22 1 45 days 5 September 5

Discount date: July 22 1 20 days 5 August 11

Cash discount: $45,000 3 0.015 5 $675

Remittance: $45,000 2 $675 5 $44,325

Loan: Interest days: August 11 to September 5 5 25 days

Interest 5 P 3 R 3 T 5 $44,325 3 0.12 35$364.32

Savings: $675 cash discount 2 $364.32 interest 5 $310.68

COMPLETE ASSIGNMENT 15.3.

365

✔

CONCEPT CHECK 15.6

bank discount loan

bearer

discounted note

discount amount

discount date

discount period

discount rate

due date

face value

interest-bearing note

interest dollars

maker

maturity date

maturity value

negotiable promissory

note

non-interest-bearing

promissory note

proceeds

promissory note

Chapter Terms for Review

THE BOTTOM LINE

Chapter 15 Promissory Notes and Discounting 307

Summary of chapter learning objectives:

Learning Objective

15.1

Compute the number of interest days of a promissory

note.

Example

1. Find the number of days between December 10 and February 27.

Answers: 1. 79 days 2. August 18 3. $6,628.22 4a. Interest, $59.18; discount, $55.64; proceeds, $8,003.54;

4b. Discount, $29.38; proceeds, $2,470.62 5. Discount, $78; proceeds, $3,822; interest rate, 12.24% 6. Due date,

April 9; discount date, March 20; cash discount, $400; remittance, $19,600; interest, $96.66; savings, $303.34

15.2

Determine the due date of a promissory note.

2. Find the due date of a 90-day note written on May 20.

15.3

Compute the maturity value of a promissory note.

3. Find the maturity value of a 90-day promissory note with a face

value of $6,500 and an exact interest rate of 8%.

15.4

Discount a promissory note.

4a. A 30-day note, bearing an interest rate of 9%, is dated November 6

and has a face value of $8,000. On November 15, the note is

discounted at 12%. Use a 365-day year to find the interest amount,

the discount amount, and the proceeds.

4b. A 60-day, non-interest-bearing note has a face value of $2,500 and

is dated May 13. On June 3, the note is discounted at 11%. Use a

365-day year to find the discount amount and the proceeds.

15.5

Compute the proceeds and actual interest rate on a

bank discount loan.

5. A 60-day bank loan with a face value of $3,900 is made on a

discount basis at a discount rate of 12%. Use the 360-day year to

compute the discount amount and the proceeds. Then find the actual

interest rate, based on the proceeds rather than on the face value.

15.6

Compute the savings from borrowing money to take a

cash discount.

6. A $20,000 invoice dated March 15 has terms of 2/5, net 25. Find the

due date, (cash) discount date, cash discount, and required remittance.

Next, calculate the interest amount of borrowing the remittance at 9%

exact interest for the time between the last date to take advantage of

the cash discount and the due date. Finally, calculate the savings.

1 A 75-day promissory note for $3,400 is dated November 24, 2010. Find (a) the due date and (b) the maturity value,

if the rate is 9% ordinary simple interest.

2 A promissory note for $4,400 is dated December 11, 2009, and has a due date of May 11, 2010. Find (a) the num-

ber of interest days and (b) the maturity value, if the rate is 7.2% ordinary simple interest.

3 A 135-day promissory note for $15,000 is dated August 24, 2011. Find (a) the due date and (b) the maturity value,

if the rate is 4.6% exact simple interest.

4 A promissory note for $2,980 is dated May 21, 2012, and has a due date of September 21, 2012. Find (a) the num-

ber of interest days and (b) the maturity value, if the rate is 6.5% exact simple interest.

5 Vernon Lee holds a 120-day, interest-bearing note for $2,960 that is dated May 15 and has a rate of 8% exact sim-

ple interest. On July 15, Vernon sells it at a discount rate of 15%. Using a 365-day year, calculate (a) the interest

amount, (b) the maturity value, (c) the maturity date, (d) the days of discount, (e) the discount amount, and (f) the

proceeds.

6 Contractor Allen Kimmel is holding a 90-day, non-interest-bearing note for $3,100 dated November 10. On Decem-

ber 10, Mr. Kimmel sells the note to Thrift’s Financing, Inc., at a discount rate of 12%. Using a 365-day year, calcu-

late (a) the maturity value, (b) the maturity date, (c) the days of discount, (d) the discount amount, and (e) the

proceeds.

7 Eastside Bank & Trust Co. made a 120-day loan for $4,500 on a discount basis, using a discount rate of 9%. Using

a 360-day year, calculate (a) the discount amount, (b) the proceeds, and (c) the actual interest rate (to two decimal

places).

8 Jankowski Corporation just received an invoice for $1,600 that has cash discount terms of 2/10, net 30. Jankowski

borrows enough money from Eastside Bank & Trust Co. at 10% exact simple interest (365-day year) to take advan-

tage of the cash discount. It borrows the money only for the time period between the due date and the last day to

take advantage of the discount. Calculate (a) the amount of the cash discount, (b) the number of interest days,

SELF-CHECK

Review Problems for Chapter 15

308 Part 4 Interest Applications

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

Chapter 15 Promissory Notes and Discounting 309

Assignment 15.1: Dates, Times, and Maturity Value

Name

Date Score

A (36 points) Problems 1–6: Find the number of interest days. Problems 7–12: Find the due date. Be sure

to check for leap years. (3 points for each correct answer)

Date of Note Due Date Days of Interest

1. April 6, 2010 October 11, 2010

2. June 29, 2012 October 5, 2012

3. February 8, 2011 June 10, 2011

4. June 15, 2009 September 14, 2009

5. November 8, 2010 March 9, 2011

6. July 17, 2012 October 5, 2012

Date of Note Days of Interest Due Date

7. November 1, 2011 90 days

8. August 18, 2010 180 days

9. September 21, 2012 75 days

10. April 29, 2010 60 days

11. November 9, 2009 120 days

12. October 31, 2011 4 months

Score for A (36)

Oct. 31, 2011 1 4 months 5 Feb. 29, 2012 (a leap year)

February 29, 2012

120 2 (30 2 9) 2 31 2 31 2 28 5 9

March 9, 2010

60 2 (30 2 29) 2 31 5 28

June 28, 2010

75 2 (30 2 21) 2 31 2 30 5 5

December 5, 2012

180 2 (31 2 18) 2 30 2 31 2 30 2 31 2 31 5 14

February 14, 2011

90 2 (30 2 1) 2 31 5 30

January 30, 2012

(31 2 17) 1 31 1 30 1 5 5 80

(30 2 8) 1 31 1 31 1 28 1 9 5 121

121

(30 2 15) 1 31 1 31 1 14 5 91

(28 2 8) 1 31 1 30 1 31 1 10 5 122

122

(30 2 29) 1 31 1 31 1 30 1 5 5 98

(30 2 6) 1 31 1 30 1 31 1 31 1 30 1 11 5 188

188

Learning Objectives

2 3

B (64 points) For each of the following promissory notes, find the missing entry for days of interest or ma-

turity date (due date).Then compute the amount of interest due at maturity and the maturity value. For

problems 13–16, use a 360-day year; for problems 17–20, use a 365-day year. (Points indicated at the top

of each column)

Face Date of Days of Maturity Interest Maturity

Value Note Interest (3 pts) Date (3 pts) Rate Amount (3 pts) Value (2 pts)

13. $26,000 Oct. 12, 2010 90 6.2%

$26,403.00$403.00Jan. 10, 2011

310 Part 4 Interest Applications

Assignment 15.1 Continued

105 2 (30 2 4) 2 31 2 31 5 17 $31,860 3 0.075 35$687.39 $31,860 1 $687.39

105

365

180 2 (28 2 11) 2 31 2 30 2 31 2 30 2 31 5 10 $52,000 3 0.0825 35$2,115.62 $52,000 1 $2,115.62

180

365

(31 2 6) 1 30 1 31 1 31 1 19 5 136 $18,420 3 0.0675 35$463.28 $18,420 1 $463.28

136

365

(30 2 24) 1 31 1 31 1 28 1 29 5 125 $41,800 3 0.051 35$730.07 $41,800 1 $730.07

125

365

(31 2 25) 1 28 1 31 1 1 5 66 $950 3 0.072 35$12.54 $950 1 $12.54

360

105 2 (31 2 15) 2 31 2 30 5 28 $35,750 3 0.056 35$583.92 $35,750 1 $583.92

105

360

(31 2 29) 1 30 1 31 1 30 1 8 5 101 $12,500 3 0.085 35$298.09 $12,500 1 $298.09

101

360

90 2 (31 2 12) 2 30 2 31 5 10 $26,000 3 0.062 35$403 $26,000 1 $403

360

Score for B (64)

20. $31,860 June 4, 2012 105 7.5%

$32,547.39$687.39Sept. 17, 2012

19. $52,000 Feb. 11, 2009 180 8.25%

$54,115.62$2,115.62Aug. 10, 2009

18. $18,420 May 6, 2011 Sept. 19, 2011 6.75%

$18,883.28$463.28136

17. $41,800 Nov. 24, 2009 Mar. 29, 2010 5.1%

$42,530.07$730.07125

16. $950 Jan. 25, 2011 April 1, 2011 7.2%

$962.54$12.5466

15. $35,750 July 15, 2009 105 5.6%

$36,333.92$583.92Oct. 28, 2009

14. $12,500 Mar. 29, 2010 July 8, 2010 8.5%

$12,798.09$298.09101

Chapter 15 Promissory Notes and Discounting 311

Assignment 15.2: Discounting Promissory Notes

Name

Date Score

A (50 points) Compute the missing information to discount the following interest-bearing and non-

interest-bearing promissory notes. Use a 360-day year for all interest and discount calculations.

(Points for each correct answer are shown in parentheses)

Learning Objective

1. Sharon Wilder had been holding a 75-day note

for $2,500. The note had a 6% interest rate and

had been written on March 1. To pay income

taxes, Sharon sold the note on April 13 to a

loan company. The loan company discounted

the note at 11%.

Interest amount (3 pts)

Maturity value (2 pts)

Maturity date (2 pts)

Days of discount (2 pts)

Discount amount (3 pts)

Proceeds (2 pts)

2. On September 10, Carol Swift Financial Services

bought a $12,500 promissory note. The note had

been written on July 10, was for 150 days, and had

an interest rate of 9%. Carol’s company discounted

the note at 12%.

Interest amount (3 pts)

Maturity value (2 pts)

Maturity date (2 pts)

Days of discount (2 pts)

Discount amount (3 pts)

Proceeds (2 pts)

$12,588.33

$380.42

Dec. 7

$12,968.75

$468.75

$2,506.50

$24.75

May 15

$2,531.25

$31.25

3. Jim Walter was holding a 105-day, non-interest-

bearing note for $4,500. The note was dated

October 9. To raise Christmas cash, Jim sold the

note to a local finance company on December

14. The company discounted the note at 10%.

Interest amount (1 pt)

Maturity value (1 pt)

Maturity date (2 pts)

Days of discount (2 pts)

Discount amount (3 pts)

Proceeds (2 pts)

4. Barbara Finell owned a finance company. On July 19

she purchased a 180-day, non-interest-bearing promis-

sory note. The note had been written on May 23 for

$7,100. Because of the high financial risk involved,

Barbara discounted the note at 14%.

Interest amount (1 pt)

Maturity value (1 pt)

Maturity date (2 pts)

Days of discount (2 pts)

Discount amount (3 pts)

Proceeds (2 pts)

$6,760.38

$339.62

123

Nov. 19

$7,100

$4,451.25

$48.75

Jan. 22

$4,500

Score for A (50)

I 5 $2,500 3 0.06 35$31.25

MV 5 $2,500 1 $31.25 5 $2,531.25

Mat. Date: 75 2 (31 2 1) 2 30 5 15

Disc. Days: (30 2 13) 1 15 5 32

D 5 $2,531.25 3 0.11 35$24.75

Proceeds 5 $2,531.25 2 $24.75 5 $2,506.50

360

I 5 $12,500 3 0.09 35$468.75

MV 5 $12,500 1 $468.75 5 $12,968.75

Mat. Date: 150 2 (31 2 10) 2 31 2 30 2 31 2 30 5 7

Disc. Days: (30 2 10) 1 31 1 30 1 7 5 88

D 5 $12,968.75 3 0.12 35$380.42

Proceeds 5 $12,968.75 2 $380.42 5 $12,588.33

360

150

360

I 5 $0; MV 5 FV 5 $4,500

Mat. Date: 105 2 (31 2 9) 2 30 2 31 5 22

Disc. Days: (31 2 14) 1 22 5 39

D 5 $4,500 3 0.10 35$48.75

Proceeds 5 $4,500 2 $48.75 5 $4,451.25

360

I 5 $0; MV 5 FV 5 $7,100

Mat. Date: 180 2 (31 2 23) 2 30 2 31 2 31 2 30 2 31 5 19

Disc. Days: (31 2 19) 1 31 1 30 1 31 1 19 5 123

D 5 $7,100 3 0.14 35$339.62

Proceeds 5 $7,100 2 $339.62 5 $6,760.38

123

360

312 Part 4 Interest Applications

Assignment 15.2 Continued

B (50 points) Compute the missing information to discount the following interest-bearing and non-

interest-bearing promissory notes. Use a 365-day year for all interest and discount calculations.

(Points for each correct answer are shown in parentheses)

As payment for services, Pat Chard held a 90-

day, 8% note for $3,600 that was dated April

20. On June 5, Pat took the note to a financial

services company, which bought the note at a

13% discount rate.

Interest amount (3 pts)

Maturity value (2 pts)

Maturity date (2 pts)

Days of discount (2 pts)

Discount amount (3 pts)

Proceeds (2 pts)

6. Joslin Builders received a 135-day, 7% note dated

October 10. The face value was $12,450, which was

for remodeling a client’s garage. On December 19,

Joslin sold the note to McGraw Lending Corp.,

which discounted the note at 12%.

Interest amount (3 pts)

Maturity value (2 pts)

Maturity date (2 pts)

Days of discount (2 pts)

Discount amount (3 pts)

Proceeds (2 pts)

$12,499.40

$272.94

Feb. 22

$12,772.34

$322.34

$3,613.48

$57.53

July 19

$3,671.01

$71.01

7. Teri Chung loaned $4,000 to a client who gave

Teri a non-interest-bearing note dated August 1.

The note was for 75 days. On August 31, Teri

sold the note to her finance company, which

discounted it at 10%.

Interest amount (1 pt)

Maturity value (1 pt)

Maturity date (2 pts)

Days of discount (2 pts)

Discount amount (3 pts)

Proceeds (2 pts)

8. Patti Gentry was holding a 60-day, non-interest-

bearing note for $1,700. The note was dated June

22. On July 16, Patti sold the note to a lender who

discounted the note at 15%.

Interest amount (1 pt)

Maturity value (1 pt)

Maturity date (2 pts)

Days of discount (2 pts)

Discount amount (3 pts)

Proceeds (2 pts)

$1,674.85

$25.15

Aug. 21

$1,700

$3,950.68

$49.32

Oct. 15

$4,000

I 5 3,600 3 0.08 35$71.01

MV 5 $3,600 1 $71.01 5 $3,671.01

Mat. Date: 90 2 (30 2 20) 2 31 2 30 5 19

Disc. Days: (30 2 5) 1 19 5 44

D 5 $3,671.01 3 0.13 35$57.53

Proceeds 5 $3,671.01 2 $57.53 5 $3,613.48

365

I 5 $0; MV 5 FV 5 $4,000

Mat. Date: 75 2 (31 2 1) 2 30 5 15

Disc. Days: (31 2 31) 1 30 1 15 5 45

D 5 $4,000 3 0.10 35$49.32

Proceeds 5 $4,000 2 $49.32 5 $3,950.68

365

I 5 $0; MV 5 FV 5 $1,700

Mat. Date: 60 2 (30 2 22) 2 31 5 21

Disc. Days: (31 2 16) 1 21 5 36

D 5 $1,700 3 0.15 35$25.15

Proceeds 5 $1,700 2 $25.15 5 $1,674.85

365

I 5 $12,450 3 0.07 35$322.34

MV 5 $12,450 1 $322.34 5 $12,772.34

Mat. Date: 135 2 (31 2 10) 2 30 2 31 2 31 5 22

Disc. Days: (31 2 19) 1 31 1 22 5 65

D 5 $12,772.34 3 0.12 35$272.94

Proceeds 5 $12,772.34 2 $272.94 5 $12,499.40

365

135

365

Score for B (50)

Chapter 15 Promissory Notes and Discounting 313

Assignment 15.3: Bank Discounting and Cash Discounts

Name

Date Score

A (36 points) The Citizens’ Bank of New England made six new loans on a discount basis. Compute the

discount amount and the proceeds.Then compute the actual interest rate based on the proceeds rather

than the face value. Use a 360-day year for problems 1–3 and use a 365-day year for problems 4–6.

Round the actual interest rates to the nearest 1/100 of a percent. (2 points for each correct answer)

Face Discount Discount Actual

alue Rate Time Amount Proceeds Interest Rate

1. $7,500 10% 120 days

2. $4,450 6% 90 days

3. $16,500 12% 150 days

4. $22,500 6.5% 60 days

5. $980 7.5% 135 days

6. $18,250 9.6% 105 days

9.87%$17,746$504

7.71%$952.82$27.18

6.57%$22,259.59$240.41

12.63%$15,675$825

6.09%$4,383.25$66.75

10.34%$7,250$250

Learning Objectives

R 5

P 3 T

$250

$7,250 3

120

360

5 0.103448

R 5

$66.75

$4,383.25 3

360

5 0.060914

R 5

$825

$15,675 3

150

360

5 0.126316

R 5

$240.41

$22,259.59 3

365

5 0.065702

R 5

$27.18

$952.82 3

135

365

5 0.077125

R 5

$504

$17,746 3

105

365

5 0.098726

$7,500 3 0.10 35$250

$7,500 2 $250 5 $7,250

120

360

$4,450 3 0.06 35$66.75

$4,450 2 $66.75 5 $4,383.25

360

$16,500 3 0.12 35$825

$16,500 2 $825 5 $15,675

150

360

$22,500 3 0.065 35$240.41

$22,500 2 $240.41 5 $22,259.59

365

$980 3 0.075 35$27.18

$980 2 $27.18 5 $952.82

135

365

$18,250 3 0.096 35$504

$18,250 2 $504 5 $17,746

105

365

Score for A (36)