General Mathematics
Quarter 2 – Module 1:
Simple Interest and
Compound Interest
General Mathematics – Grade 11
Alternative Delivery Mode
Quarter 2 – Module 1: Simple Interest and Compound Interest
First Edition, 2020
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SENIOR HS MODULE DEVELOPMENT TEAM
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General Mathematics
Quarter 2 – Module 1:
Simple Interest and Compound
Interest
Introductory Message
For the facilitator:
Welcome to the General Mathematics – Grade 11 Alternative Delivery Mode (ADM)
Module on Simple Interest and Compound Interest!
This module was collaboratively designed, developed and reviewed by educators both
from public and private institutions to assist you, the teacher or facilitator in helping
the learners meet the standards set by the K to 12 Curriculum while overcoming
their personal, social, and economic constraints in schooling.
This learning resource hopes to engage the learners into guided and independent
learning activities at their own pace and time. Furthermore, this also aims to help
learners acquire the needed 21st century skills while taking into consideration their
needs and circumstances.
In addition to the material in the main text, you will also see this box in the body of
the module:
Notes to the Teacher
This contains helpful tips or strategies
that will help you in guiding the learners.
As a facilitator you are expected to orient the learners on how to use this module.
You also need to keep track of the learners' progress while allowing them to manage
their own learning. Furthermore, you are expected to encourage and assist the
learners as they do the tasks included in the module.
1
For the learner:
Welcome to the General Mathematics – Grade 11 Alternative Delivery Mode (ADM)
Module on Simple Interest and Compound Interest!
The hand is one of the most symbolized part of the human body. It is often used to
depict skill, action and purpose. Through our hands we may learn, create and
accomplish. Hence, the hand in this learning resource signifies that you as a learner
is capable and empowered to successfully achieve the relevant competencies and
skills at your own pace and time. Your academic success lies in your own hands!
This module was designed to provide you with fun and meaningful opportunities for
guided and independent learning at your own pace and time. You will be enabled to
process the contents of the learning resource while being an active learner.
This module has the following parts and corresponding icons:
What I Need to Know
This will give you an idea of the skills or
competencies you are expected to learn in the
module.
What I Know
This part includes an activity that aims to
check what you already know about the
lesson to take. If you get all the answers
correct (100%), you may decide to skip this
module.
What’s In
This is a brief drill or review to help you link
the current lesson with the previous one.
What’s New
In this portion, the new lesson will be
introduced to you in various ways such as a
story, a song, a poem, a problem opener, an
activity or a situation.
What is It
This section provides a brief discussion of the
lesson. This aims to help you discover and
understand new concepts and skills.
What’s More
This comprises activities for independent
practice to solidify your understanding and
skills of the topic. You may check the
answers to the exercises using the Answer
Key at the end of the module.
What I Have Learned
This
includes
questions
or
blank
sentence/paragraph to be filled in to process
what you learned from the lesson.
What I Can Do
This section provides an activity which will
help you transfer your new knowledge or skill
into real life situations or concerns.
2
Assessment
This is a task which aims to evaluate your
level of mastery in achieving the learning
competency.
Additional Activities
In this portion, another activity will be given
to you to enrich your knowledge or skill of the
lesson learned. This also tends retention of
learned concepts.
Answer Key
This contains answers to all activities in the
module.
At the end of this module you will also find:
References
This is a list of all sources used in developing
this module.
The following are some reminders in using this module:
1. Use the module with care. Do not put unnecessary mark/s on any part of the
module. Use a separate sheet of paper in answering the exercises.
2. Don’t forget to answer What I Know before moving on to the other activities
included in the module.
3. Read the instruction carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking your answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are through with it.
If you encounter any difficulty in answering the tasks in this module, do not
hesitate to consult your teacher or facilitator. Always bear in mind that you are
not alone.
We hope that through this material, you will experience meaningful learning and
gain deep understanding of the relevant competencies. You can do it!
3
What I Need to Know
At the end of the lesson, the students are expected:
•
•
illustrate simple and compound interests (M11GM-IIa-1); and
distinguish between simple and compound interests (M11GM-11a-2).
What I Know
MULTIPLE CHOICE: Choose the letter of the correct answer.
1. The amount of money borrowed or invested on the origin date.
a. rate
c. future value
b. principal
d. interest
2. The amount of time in years when the money is borrowed or invested.
a. term
c. maturity date
b. origin date
d. rate
3. The person or institution that invests the money or makes the funds
available.
a. lender
c. borrower
b. collector
d. debtor
4. The amount after t years that the lender receives from the borrower on
maturity date.
a. present value
c. maturity value
b. rate
d. principal
5. It is based on a 30-day month computation.
a. actual time
c. ordinary interest
b. approximate time
d. exact interest
6. Find the actual time from February 20, 2018 to December 15, 2018.
a. 296 days
c. 298 days
b. 297 days
d. 299 days
4
7. Find the approximate time from October 23, 2018 to June 9, 2019.
a. 225 days
c. 227 days
b. 226 days
d. 228 days
8. How much simple interest would acquire the an amount of PHP 10, 000
after 6 years at a rate of 3%?
a. PHP 1,500.00
c. PHP 1,900.00
b. PHP 1,800.00
d. PHP 2,100.00
9. Suppose you invested PHP 35, 000 at a simple rate of 2.5%, how much will
be your investment after 10 years?
a. PHP 43,750.00
c. PHP 45,730.00
b. PHP 45,370.00
d. PHP 47,350.00
10. Peter borrowed PHP 153, 000 at 8% compounded annually. How much he
will be paying after 3 years?
a. PHP 129, 375.49
c. PHP 195, 372.94
b. PHP 192, 735.94
d. PHP 197, 273.94
Notes to the Teacher
This module gives the learners the concept of simple and compound
interests.
5
Lesson
1
Illustrating Simple and
Compound Interests
Money cannot be borrowed all the time. Borrowing money might be a crucial decision
for someone who has a certain needs and purposes. But how much does it cost to
borrow money? In this regard, the idea of paying interest comes in. Paying interest
is paying for the use of money you borrowed under a certain circumstance. This has
been a part of human activities since time immemorial. It has been regarded as
legitimate commercial practice of all people in different walks of life. As an individual,
it is essential to understand how you can make your money works - a gain or a loss
in the lending and borrowing money industry.
What’s In
Change the following expressions into another form.
A. Express the following percent in decimal form.
1. 5%
2. 12%
3. 2.3%
4. 6.75%
5. 0.7%
B. Change the following decimals in percent form.
1. 0.25
2. 0.3
3. 2.7
4. 0.06
5. 0.0009
C. Express the following number of days and months in years.
1. 85 days
2. 267 days
3. 305 days
4. 10 months
5. 7 and a half months
6
What’s New
Unlock the 8-letter word by finding the similarities of each of the following
illustrations. Write your answer inside the boxes provided below.
Source: https://images.google.com/
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What is It
Definition of Terms
Here are some important terms to remember.
1. Interest (I) – the amount paid or earned for the use of money.
2. Simple Interest (Is) – it is the interest that is computed on the principal and
then added to it.
3. Compound Interest (Ic) – the interest is computed on the principal and on the
accumulated past interests.
4. Principal (P) – the amount of money borrowed or invested on the origin date.
5. Rate (r) – the annual rate, usually in percent, charged by the lender, or rate of
increase of the investment.
6. Time or Term (t) – It is the amount of time in years the money is borrowed or
invested, length of time between the origin and maturity dates.
7. Maturity value or future value (F) – It is amount after t years that the lender
receives from the borrower on the maturity date.
8. Origin or loan date – The date on which money is received by the borrower.
9. Maturity date – The date on which the money borrowed, or loan is to be
completely repaid.
10. Lender o creditor – The person (or institution) that invests the money or makes
the funds available.
11. Borrower or debtor – The person (or institution) that owes the money or avails
of the funds from the lender.
Illustration of Simple and Compound Interest
Suppose you plan to invest 20,000.00 pesos for 5 years. The first bank offers
you 3% simple interest rate per year while the second bank offers 3% compounded
annually. Study how the interest is computed to help you decide which bank you
decide to choose to invest your money.
BANK A: SIMPLE INTEREST
P
r
t
Solution
Interest
Future Value
20, 000
3%
1
(20,000 x .03 x 1)
600
20,600
8
P
r
t
Solution
Interest
Future Value
20, 000
3%
2
(20,000 x .03 x 2)
1,200
21, 200
P
r
t
Solution
Interest
Future Value
20, 000
3%
3
(20,000 x .03 x 3)
1, 800
21,800
P
r
t
Solution
Interest
Future Value
20, 000
3%
4
______________________
___________
__________________
P
r
t
Solution
Interest
Future Value
20, 000
3%
5
______________________
___________
__________________
You may now continue solving up to the 5th year, if you finally arrived at PHP 23,
000.00.
It is a good job!
Now you can check out how much interest Bank B can offer you.
BANK B: COMPOUND INTEREST
P
r
t
Solution
Interest
Future Value
20, 000
3%
1
(20,000 x .03 x 1)
600
20,600
P
r
t
Solution
Interest
Future Value
20, 600
3%
1
(20,600 x .03 x 1)
618
20,600 + 618
= 21, 218
9
P
r
t
Solution
Interest
Future Value
21, 218
3%
1
(21, 218 x .03 x 1)
636.54
21,218 + 636.54 =
21, 854.54
P
r
t
Solution
Interest
Future Value
___________
3%
1
(_____________ x .03 x 1)
P
r
t
Solution
Interest
Future Value
___________
3%
1
(_____________ x .03 x 1)
___________
__________________
___________ __________________
Again, continue solving up to 5th year, see if you will also get PHP 23, 185.48. If so,
then give yourself an applause for doing it right!
Take Note: Simple interest remains constant throughout the investment term. In
compound interest, the interest from the previous year also earns interest. Thus, the
interest grows every year.
Can you now decide which bank you invest your money? Be sure to make the right
and wise choice.
Actual Time and Approximate Time
In computing interest, time or term is an important element in any financial
transaction. Time can be classified as actual time and approximate time. Both terms
can greatly affect the computation of interest. Refer to the given definitions below:
•
•
Actual time – refers to the actual number of days between two given
dates.
Approximate time – considers each month as having 30 days.
10
Now, you see how this works. For instance, a loan transaction was made on July 26,
2019 and matured on November 8, 2019. Compute the actual time and approximate
time.
ACTUAL TIME
July 26, 2019 =
APPROXIMATE TIME
5 days (31 - 26 = 5)
July 26, 2019 =
4 days (30-26=4)
August
31 days
August
30 days
September
30 days
September
30 days
October
31 days
October
30 days
November
8 days
November
8 days
Total
105 days
Total
102 days
Try another one, find the actual time and approximate time from January 13, 2020
to September 19, 2020.
ACTUAL TIME
APPROXIMATE TIME
January 13
18 days
January 13
17 days
February
28 days
February
30 days
March
31 days
March
30 days
April
30 days
April
30 days
May
31 days
May
30 days
June
30 days
June
30 days
July
31 days
July
30 days
August
31 days
August
30 days
September
19 days
September
19 days
Total
249 days
Total
246 days
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What’s More
A. WORD HUNT
Arrange the jumbled letters to form 15 words which are related to simple and
compound interest. The words may be hidden in the grid in any direction.
I
A
S
B
I
A
N
A
F
A
E
H
N
E
R
O
M
N
A
D
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S
T
A
V
E
G
R
N
N
T
A
T
B
T
E
E
T
B
R
F
U
R
E
U
M
R
L
S
M
N
O
C
A
E
T
R
U
A
S
T
A
J
W
O
L
L
N
E
E
N
R
A
T
U
E
I
N
A
O
V
T
S
A
R
U
S
R
L
I
N
K
A
H
A
T
P
R
I
N
C
I
P
A
L
N
C
E
M
I
T
Y
U
F
S
E
U
T
T
A
A
T
A
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R
M
R
E
T
I
R
T
Y
M
A
D
I
A
B
C
D
O
E
U
D
E
B
T
O
R
D
T
U
N
D
R
A
E
X
A
C
T
L
M
E
I
N
I
T
F
U
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I
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C
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12
B. Complete the table.
SIMPLE INTEREST
P
r
t
15, 000
5%
1
Solution
Interest
Future Value
Interest
Future Value
COMPOUND INTEREST
P
r
t
15, 000
5%
1
Solution
C. Find the actual time and approximate time from August 25, 2019 to April 11,
2020.
13
What I Have Learned
Using Venn Diagram below, give the similarities and differences between simple
interest and compound interest.
SIMPLE INTEREST
COMPOUND INTEREST
14
What I Can Do
Accomplish a reflection journal using the given images below.
15
Assessment
Solve the following word problems.
1. How much interest would your money earn if you deposited PHP 25,
000. 00 at a simple rate of 3% given the actual date from June 6, 2020
to March 25, 2021.
2. During this time of pandemic, many lending institutions offer a loan
package to wage earners. Suppose loan company ABC offers you to
borrow money amounting to PHP 50, 000 and payable in 4 years at a
simple interest rate of 3% per annum, while loan company XYZ offers a
3% compounded annually. What loan company will you borrow money,
then justify why you decide to choose to make loan with that particular
loan company.
16
Additional Activities
Match each set of triangles to form a logical computation of a bigger triangle that
includes the Principal, Time, Rate, and Interest.
Principal
37, 500.00
Principal
15,000.00
Principal
12,000.00
Time
2.5 years
Time
9 months
Time
5 years
Rate
5.3%
Interest
6, 093.75
Rate
6.5%
Interest
2, 250.00
17
Rate
3%
Interest
477.00
18
Additional Activities:
P – 37,500.00
R – 6.5%
T – 2.5 years
I – 6,093.75
What’s More:
Assessment:
1.
2.
P – 15,000.00
R – 3%
T – 5 years
I – 2,250.00
PHP 600.00
Lending institution A:
PHP 56,000.00
Lending institution B:
PHP 56, 275.44
P – 12,000.00
R – 5.3%
T – 9 months
I - 477
What’s More:
A. Invest
Borrower
Annual
Future value
Transaction
Rate
Maturity date
Lender
Interest
Loan
Principal
Time
Term
Debtor
Actual time
Future Value:
PHP 15,750.00
PHP 16,537.50
PHP 17,364.38
Interest:
PHP 750.00
PHP 787.50
PHP 826.88
Future Value
PHP 15,750.00
PHP 16,500.00
PHP 17,250.00
B.
Interest:
PHP 750.00
PHP 1,500.00
PHP 2,250.00
C.
Actual Time: 229 days
Approximate Time: 226 days
What’s In:
A.
1. 0.05
2. 0.12
3. 0.023
4. 0.0675
5. .007
B.
1. 25%
2. 30%
3. 270%
4. 6%
5. 0.09%
C.
1. 0.24
2. 0.73
3. 0.8U
4 0.83
5. 0625
What’s New
INTEREST
What is It:
Simple Interest
Interest:
PHP 2,400.00
PHP 3,000.00
Future Value:
PHP 22,400.00
PHP 23,000.00
Compound Interest
Interest:
PHP 655.64
PHP 675.30
Future Value:
PHP 22,510.18
PHP 23,185.48
What I Know:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
B
A
A
C
B
C
B
B
A
B
Answer Key
19
What’s More:
A.
References
DepEd (2016). General Mathematics: Learner’s Material (English).First Edition.
Phoenix Publishing House (2016). Next Century Mathematics: General
Mathematics.
Vibal Group Inc.(2016). General Mathematics.
DepEd (2020). Most Essential Learning Competencies.
https://www.canva.com/design/DAEJg6zaG14/7BdhJxfHJi_sxP5yg8mAg/edit?cat
egory=tACZCgsdcSU#
https://www.coursehero.com/file/p18q8bl/Exact-and-Ordinary-Interest-Actualand-Approximate-Time-Exact-Interest-refers/
https://www.google.com/search?q=venn+diagram+template&safe=active&rlz=1C1C
HZL_enPH898PH900&tbm=isch&source=iu&ictx=1&fir=O51Zq6GjOnX44M%252Cz
Z1er_Li-DiY6M%252C_&vet=1&usg=AI4_-kRcVD0_FxlQbg0i0PjuUx-wt92nQ&sa=X&ved=2ahUKEwje4NDBwJfsAhUCGaYKHQwmAKQQ9QF6BAgNEFw&b
iw=1366&bih=608#imgrc=O51Zq6GjOnX44M
20
For inquiries or feedback, please write or call:
Department of Education – Region III,
Schools Division of Bataan - Curriculum Implementation Division
Learning Resources Management and Development Section (LRMDS)
Provincial Capitol Compound, Balanga City, Bataan
Telefax: (047) 237-2102
Email Address: bataan@deped.gov.ph