310 chapter 10 • Simple intereSt and promiSSorY noteS
determining the matUritY
date of a loan
When the loan date and number of days of the loan are known, the maturity date can be found
as follows:
10-5
StepS For DeTermInIng The maTUrITy DaTe oF a Loan
Step 1. Find the number of days remaining in the first month by subtracting the loan
date from the number of days in that month.
ExamplE6
determining matUritY
date oF a loan
What is the maturity date of a loan taken out on april 14 for 85 days?
SolutionStrategy
Step 1. Days remaining in first month
30
Days in April
−14
Loan date April 14
Days remaining in April
16
Step 2. Subtract remaining days in first
38
38
8
8
85
Days of the loan
tryitexerciSe 6
a. What is the maturity date of a loan taken out on September
9
for
125
days?
10%
80
RevIew exeRcISeS
Find the amount of interest on each of the following loans.
Principal Rate (%) Time Interest
1.
$5,000
8
2
years
$800.00
$100,000
10
in the
Business World
Section i
Learning Tip
Section i
85461_ch10_hr_304-312_1.indd 310 9/23/15 4:52 PM
Section i • UnderStanding and compUting Simple intereSt 311
Principal Rate (%) Time Interest
Principal Rate (%) Time (days) Exact Interest Ordinary Interest
7.
$45,000
13
100
$1,602.74
$1,625.00
$184,500
7.75
58
8.6
$7,230
9
18
60
6
14.1
230
$50,490
69
Find the amount of interest and the maturity value of the following loans. Use the formula
MV =P+I
to find the maturity values.
Principal Rate (%) Time Interest Maturity Value
17.
11.9
2
years
$12,852.00
$66,852.00
$125,000
5
Find the maturity value of the following loans. Use
MV =P(1 +RT
)
to find the maturity
values.
Principal Rate (%) Time Maturity Value
23.
$1,500
9
2
years
$1,770.00
$1,000,000
11
$5,200
From the following information, determine the number of days of each loan.
Loan Date Due Date Number of Days
29. September 5 December
12
98
2
Exercises 4–34 appear in Appendix B.
312 chapter 10 • Simple intereSt and promiSSorY noteS
Complete worked-out solutions for
Exercises 35–41 appear in Appendix B.
holdersare the owners of the credit
union. Credit unions serve groups that
share something in common, such as
Virginia, with
$36.4
billion in assets and
3.2
 million members.
RosaIreneBetancourt 1/Alamy
From the following information, determine the maturity date of each loan.
Loan Date Time of Loan (days) Maturity Date
110
26
29
200
79
87
Solve the following word problems. round to the nearest cent when necessary.
42. On April 12, Michelle Lizaro borrowed
$5,000
from her credit union at
9%
for
80
days. The
credit union uses the ordinary interest method.
a. What is the amount of interest on the loan?
b. What is the maturity value of the loan?
c. What is the maturity date of the loan?
43. What is the maturity value of a
$60,000
loan for
100
days at
6.1%
interest using the exact
44. Central Auto Parts borrowed
$350,000
at
9%
interest on July
19
for
120
days.
a. If the bank uses the ordinary interest method, what is the amount of interest on the loan?
b. What is the maturity date?
45. Emil Benson missed an income tax payment of
$9,000
. The Internal Revenue Service charges a
13%
simple interest penalty calculated by the exact interest method. If the tax was due on
April
15
but was paid on August
19
, what was the amount of the penalty charge?
46. At the City National Credit Union, a
7%
,
$8,000
loan for
180
days had interest charges of
. What type of interest did City National use, ordinary or exact?
47. Kyle Rohrs borrowed
$1,080
on June
16
at
9.2%
exact interest from the Wells Fargo Bank. On
August
10
, Kyle repaid the loan. How much interest did he pay?
Section ii • USing the Simple intereSt FormUla 313
Using the simple interest FormUla
In Section I, we used the simple interest formula,
I=PRT
, to solve for the interest. Frequently
in business, however, the principal, rate, or time might be the unknown factor. Remember
from Chapter 5 that an equation can be solved for any of the variables by isolating that vari-
able to one side of the equation. In this section, we convert the simple interest formula to
equations that solve for each of the other variable factors.
solving For the principal
10-6
When using the simple interest formula to solve for principal,
P
, we isolate the
P
on one side of
the equation by dividing both sides of the equation by
RT
. This yields the new equation as follows:
Business Decision: competing Banks
48. You are the accounting manager for Kool Ragz, Inc., a manufacturer of men’s and women’s
clothing. The company needs to borrow
$1,800,000
for
90
days in order to purchase a large
quantity of material at “closeout” prices. The interest rate for such loans at your bank, Rimrock
Bank, is
11%
using ordinary interest.
a. What is the amount of interest on this loan?
b. After making a few “shopping” calls, you find that Southside National Bank will lend at
11%
using exact interest. What is the amount of interest on this offer?
365
c. So that you can keep your business, Rimrock Bank has offered a loan at
10.5%
using
ordinary interest. What is the amount of interest on this offer?
d. (Challenge) If Southside National wants to beat Rimrock’s last offer (part c) by charging
$1,250
less interest, what rate, rounded to the nearest hundredths of a percent, must it quote
using exact interest?
There are approximately
7,000
© Pavel L Photo and Video/Shutterstock.com
Section ii
10
85461_ch10_hr_304-340_2.indd 313 9/23/15 4:52 PM
318 chapter 10 • Simple intereSt and promiSSory noteS
Step 5. Once all partial payments have been credited, we find the maturity value of the loan
by calculating the interest due from the last partial payment to the maturity date and
adding it to the last adjusted principal.
Note: The last partial payment was made on day
70
of the loan; therefore,
50
days
tryitexerciSe 10
Rita Peterson borrowed
at
12%
ordinary interest for
100
days. On day
20
of the loan,
shemade a partial payment of
$4,000
. On day
60
, she made another partial payment of
$5,000
.
$675
8
$3,000
8.6
5
6
6
$2,250
3
$8,190
Review exeRcises
Compute the principal for the following loans. Use ordinary interest when time is stated
in days.
Principal Rate (%) Time Interest
1. $1,250
12
2
years
$300
Compute the rate for the following loans. Round answers to the nearest tenth of a percent;
use ordinary interest when time is stated in days.
Principal Rate (%) Time Interest
8.
$5,000
8
3
years
$1,200
$1,800
5
$2,000
$295,500
$39,800
10
Section ii
85461_ch10_hr_304-340_2.indd 318 9/23/15 4:52 PM
Section ii • USing the Simple intereSt FormUla 319
$16,000
13
$760
9.5
100
$340
$3,800
165
$220
300
10.4
$4,000
Use the ordinary interest method to compute the time for the following loans. Round answers
to the next higher day when necessary.
Principal Rate (%) Time Interest
15.
$18,000
12
158 days
$948
Calculate the missing information for the following loans. Round percents to the nearest
tenth and days to the next higher day when necessary.
Principal Rate (%)
Time
(days)
Interest
Method Interest
Maturity
Value
Solve the following word problems. Round answers to the nearest cent when necessary.
27. Kendall Motors, a Buick dealership, borrowed
$225,000
on April
16
to purchase a shipment of
new cars. The interest rate was
9.3%
using the ordinary interest method. The amount of interest
was
$9,600
.
a. For how many days was the loan?
b. What was the maturity date of the loan?
28. Mike Drago took out a loan for
$3,500
at the Gold Coast Bank for
270
days. If the bank
usesthe ordinary interest method, what rate of interest was charged if the amount of
interestwas
$269
? Round your answer to the nearest tenth of a percent.
29. Tiffany Francis borrowed money from her credit union to buy a car at
13.5%
simple
interest.Ifthe loan was repaid in
2
years and the amount of interest was
$2,700
, how
muchdidTiffany borrow?
repayment of a loan. Collateral serves
as protection for a lender against a
borrower’s risk of default.
estate that is acquired with the help
of the loan serves as collateral.
Dollars
and Sense
85461_ch10_hr_304-340_2.indd 319 9/23/15 4:52 PM
$7,900
10.4
$228
$4,500
$375
$25,000
$4,450
$7,400
9.6
$200
$41,000
6.4
$3,936
$3,600
14.3
$125
has been ranked the number
one hair care franchise in
the United States and the
fifth best franchise
opportunity overall in
$111,000−$239
$100,000
Supercuts is owned by
Regis Corporation, global
leader in salon andhair
12,800
locations. With approximately
55,000
full-time employees, typical annual
revenues for Regis Corporation total
30. What is the maturity date of a loan for
$5,000
at
15%
exact interest taken out on June
3
? The
amount of interest on the loan was
$150
.
31. You are the owner of a Supercuts Hair Salon. What rate of interest were you charged on an
ordinary interest loan for
$135,000
in equipment if the interest was
$4,400
and the time period
was from January
16
to April
27
? Round your answer to the nearest tenth of a percent.
32. Michelle Payne deposited
$8,000
in a savings account paying
6.25%
simple interest. How long
will it take for her investment to amount to
$10,000
?
33. The Actor’s Playhouse theater borrowed
$100,000
at
8%
ordinary interest for
90
days to pur-
chase new stage lighting equipment. On day
40
of the loan, the theater made a partial payment
of
. What is the new maturity value of the loan?
34. Steve Perry borrowed
at
12%
ordinary interest for
60
days. On day
20
of the loan,
Steve made a partial payment of
$4,000
. What is the new maturity value of the loan?
35. Pamela Boyd borrowed
at
6.5%
ordinary interest for
150
days. On day
30
of the loan,
she made a partial payment of
$8,000
. What is the new maturity value of the loan?
36. The Mutt Hut Pet Shop borrowed
on March
15
for
90
days. The rate was
13%
using the ordinary interest method. On day
25
of the loan, The Mutt Hut made a partial
payment of
$16,000
, and on day
55
of the loan, The Mutt Hut made a second partial payment
of
.
a. What is the new maturity value of the loan?
85461_ch10_hr_304-340_2.indd 320 9/23/15 4:52 PM
Section ii • USing the Simple intereSt FormUla 321
Business Decision: the oppoRtunity cost
38. You are the owner of four Taco Bell restaurant locations. You have a business loan with
Citizens Bank taken out
60
days ago that is due in
90
days. The amount of the loan is
, and the rate is
9.5%
using ordinary interest.
You currently have some excess cash. You have the choice of sending Citizens
$25,000
now
as a partial payment on your loan or purchasing an additional
of serving supplies such
as food containers, cups, and plastic dinnerware for your inventory at a special discount price
that is “
10%
off” your normal cost of these items.
a. How much interest will you save on this loan if you make the partial payment and don’t
purchase the additional serving supplies?
b. How much will you save by purchasing the discounted serving supplies and not making the
partial payment?
c. (Optional) What other factors should you consider before making this decision?
each year in more than
5,800
restaurants in the
United States. The initial
investment to franchise
a Taco Bell is
$1.3
million
−$2.3
million. Franchise
fees are
$45,000
initial fee,
then
5.5%
monthly royalty
fees and
4.5%
monthly
advertising fees.
yum! Brands, Inc., based
in Louisville, Kentucky,
is the world’s largest
restaurant company in
terms of system restaurants,
b. What is the maturity date of the loan?
37. a. How many years will it take
$5,000
invested at
8%
simple interest to double to
$10,000
?
b. How long will it take if the interest rate is increased to
10%
?
37,000
Section iii • UnderStanding PromiSSory noteS and diScoUnting 327
b.
Purchase price =Face value −Interest
c.
E
ffective interest rate =
Interest
Purchase price ×Time
tryitexerciSe 14
Bob Schaller purchased
in U.S. Treasury bills with a discount rate of
4.6%
for a period
of
26
weeks.
a. How much interest did Bob earn on the T-bill investment?
b. How much was the purchase price of Bob’s T-bills?
c. What was the effective interest rate of Bob’s T-bill investment? Round to the nearest hundredth
of a percent.
CheCk your ANswers wITh The soluTIoNs oN PAge 335.
REVIEW EXERCISES
calculate the bank discount and proceeds for the following simple discount notes. use the
ordinary interest method,
360
days, when applicable.
Face Value Discount Rate (%) Term Bank Discount Proceeds
1.
$4,500
13
6
months $292.50 $4,207.50
11.3
50
$2,000
11
$7,800
130
using ordinary interest,
360
days, calculate the missing information for the following simple
discount notes.
Face
Value
Discount
Rate (%)
Date of
Note
Term
(days)
Maturity
Date
Bank
Discount Proceeds
6.
10
June
3
80
Aug. 22 $373.33 $16,426.67
$5,000
14.7
16
12.1
3
$1,300
5
53
using ordinary interest,
360
days, calculate the bank discount, proceeds, and effective rate
for the following simple discount notes. Round effective rate to the nearest hundredth of a
percent.
Face
Value
Discount
Rate (%)
Term
(days)
Bank
Discount Proceeds
Effective
Rate (%)
11.
$2,700
14
126
$132.30 $2,567.70 14.72
$6,505
73
10
SECTION III
328 CHAPTER 10 • SimPlE inTEREST And PRomiSSoRy noTES
Face
Value
Interest
Rate (%)
Date of
Note
Term of
Note (days)
Maturity
Date
Maturity
Value
Date of
Discount
Discount
Period (days)
Discount
Rate (%) Proceeds
16.
$2,500
12
Mar.
4
70
May 13 $2,558.33 Apr. 15 28
13
$2,532.46
Face
Value
Discount
Rate (%)
Term
(days)
Bank
Discount Proceeds
Effective
Rate (%)
$3,800
7.25
140
$95,000
45
$57,500
230
the following interest-bearing promissory notes were discounted at a bank by the payee
before maturity. use the ordinary interest method,
360
days, to calculate the missing
information.
Complete worked-out solutions for
Exercises 13–25 appear in Appendix B.
calculate the interest, purchase price, and effective interest rate of the following treasury bill
(t-bill) purchases. Round effective interest rate to the nearest hundredth of a percent.
Face
Value
Discount
Rate (%)
Term
(weeks) Interest
Purchase
Price
Effective
Rate (%)
21.
4.40
26
4.82
13
3.80
4
$100,000
4.15
26
5.20
13
$195 $14,805 5.27
use the ordinary interest method,
360
days, to solve the following word problems. Round to
the nearest cent when necessary.
26. Roni Lockard signed a
simple discount promissory note at the Pacific National Bank.
The discount rate was
11%
, and the note was made on February
17
(not in a leap-year) for
107
days.
a. What proceeds will Roni receive on the note?
b. What is the maturity date of the note?
27. Boz Foster signed a
simple discount promissory note at a bank discount rate of
6%
. If
the term of the note was
125
days, what was the effective interest rate of the note? Round your
answer to the nearest hundredth of a percent.
85461_ch10_hr_304-340_3.indd 328 9/23/15 4:53 PM
50
15
7
125
16.5
$8,000
10
10.2
$1,240
7.6
12
140
11.8
Section iii • UnderStanding PromiSSory noteS and diScoUnting 329
BUSINESS DECISION: FINaNCINg THE DEalERS
30. Richie Powers is the owner of American Eagle Boats, a manufacturer of custom pleasure
boats.Because of the economic recession and slow boat sales recently, American Eagle has begun
accepting promissory notes from its dealers to help finance large orders. This morning American
Eagle accepted a
90
-day,
9.5%
promissory note for
$600,000
from Champion Marine, one of its
sales dealers.
You are a manager for Atlantic Bank, and Richie is one of your clients. Atlantic’s discount
rate is currently
16%
. Richie’s goal is to discount the note as soon as possible, but not until the
proceeds are at least equal to the face value of the note,
$600,000
.
a. As his banker, Richie has asked you to “run the numbers” at ten-day intervals starting with
day
20
and advise him as to when he can discount the note and still receive his
$600,000
.
28. Pinnacle Manufacturing received a
promissory note at
12%
simple interest for
95
days from one of its customers. On day
70
, Pinnacle discounted the note at the Berryville
Bank at a discount rate of
15%
. The note was made on September
12
.
a. What was the maturity date of the note?
b. What was the maturity value of the note?
c. What was the discount date of the note?
d. What proceeds did Pinnacle receive after discounting the note?
29. Christy Thomas purchased
$150,000
in U.S. Treasury bills with a discount rate of
4.2%
for a
period of
4
weeks.
a. How much interest did Christy earn on the T-bill investment?
b. How much was the purchase price of Christy’s T-bills?
c. What was the effective interest rate of Christy’s T-bill investment? Round to the nearest
hundredth of a percent.
North Carolina, and New york. Typical sales
and service expenditures for recreational
boating exceed
$30
billion annually.
85461_ch10_hr_304-340_3.indd 329 9/23/15 4:53 PM
330 CHAPTER 10 • SimPlE inTEREST And PRomiSSoRy noTES
chaPter formUlas
Simple Interest
Interest =Principal ×Rate ×Time
The Simple Interest Formula
P
rincipal =
Interest
Rate ×Time
Simple Discount Notes
Bank discount =Face value ×Discount rate ×Time
Discounting a Note before Maturity
Bank discount =Maturity value ×Discount rate ×Time
P
roceeds
=
Maturity value
−
Bank discount
Purchasing U.S. Treasury Bills
10
chapter
b. (Challenge) Calculate the exact day the note should be discounted to meet Richie’s goal.
85461_ch10_hr_304-340_3.indd 330 9/23/15 4:53 PM
M
M