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General Mathematics Quarter 2 – Module 1:

Simple Interest and

Compound Interest

SENIOR HS MODULE DEVELOPMENT TEAM

Author : Liza B. Bantay

Co-Author - Content Editor : Ma. Lourdes L. Agkis

Co-Author - Language Reviewer : Efren M. Bacani

Co-Author - Illustrator : Noel S. Sarili

Co-Author - Layout Artist : Cherryl D. Cordova

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Education Program Supervisor, LRMDS : Edgar E. Garcia, MITE

Education Program Supervisor, AP/ADM : Romeo M. Layug

Education Program Supervisor, Mathematics : Danilo C. Caysido

Project Development Officer II, LRMDS : Joan T. Briz

Division Librarian II, LRMDS : Rosita P. Serrano

General Mathematics – Grade 11 Alternative Delivery Mode Quarter 2 – Module 1: Simple Interest and Compound Interest First Edition, 2020

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Office Address: Provincial Capitol Compound, Balanga City, Bataan Telefax: (047) 237-2102

E-mail Address: [email protected]

General Mathematics Quarter 2 – Module 1:

Simple Interest and Compound

Interest

1

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:

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.

Notes to the Teacher

This contains helpful tips or strategies

that will help you in guiding the learners.

2

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.

3

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:

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!

References This is a list of all sources used in developing

this module.

4

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

5

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.

6

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

7

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/

8

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

9

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% 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 ______________________ ___________ __________________

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

10

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.

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) ___________ __________________

11

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 APPROXIMATE TIME

July 26, 2019 = 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

12

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 U 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 E E 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 T U R E Y O U E

T E M I T L A U T C A L

13

B. Complete the table.

SIMPLE INTEREST

P r t Solution Interest Future Value

15, 000 5% 1

COMPOUND INTEREST

P r t Solution Interest Future Value

15, 000 5% 1

C. Find the actual time and approximate time from August 25, 2019 to April 11,

2020.

14

What I Have Learned

Using Venn Diagram below, give the similarities and differences between simple

interest and compound interest.

SIMPLE INTEREST COMPOUND INTEREST

15

What I Can Do

Accomplish a reflection journal using the given images below.

16

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.

17

Additional Activities

Match each set of triangles to form a logical computation of a bigger triangle that

includes the Principal, Time, Rate, and Interest.

Interest

2, 250.00

Rate

5.3%

Principal

12,000.00

Time

9 months

Time

2.5 years

Principal

37, 500.00

Rate

6.5%

Interest

6, 093.75

Principal

15,000.00

Interest

477.00

Time

5 years

Rate

3%

18

Answer Key

What I Know:

1.B

2.A

3.A

4.C

5.B

6.C

7.B

8.B

9.A

10.B

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’s More:

A.Invest

Borrower

Annual

Future value

Transaction

Rate

Maturity date

Lender

Interest

Loan

Principal

Time

Term

Debtor

Actual time

What’s More:

B.

Interest: Future Value

PHP 750.00 PHP 15,750.00

PHP 1,500.00 PHP 16,500.00

PHP 2,250.00 PHP 17,250.00

Interest: Future Value:

PHP 750.00 PHP 15,750.00

PHP 787.50 PHP 16,537.50

PHP 826.88 PHP 17,364.38

C.

Actual Time: 229 days

Approximate Time: 226 days

Assessment:

1.PHP 600.00

2.Lending institution A:

PHP 56,000.00

Lending institution B:

PHP 56, 275.44

Additional Activities:

P – 37,500.00

R – 6.5%

T – 2.5 years

I – 6,093.75

P – 15,000.00

R – 3%

T – 5 years

I – 2,250.00

P – 12,000.00

R – 5.3%

T – 9 months

I - 477

19

What’s More:

A.

20

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-Actual-

and-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-w-

t92nQ&sa=X&ved=2ahUKEwje4NDBwJfsAhUCGaYKHQwmAKQQ9QF6BAgNEFw&b

iw=1366&bih=608#imgrc=O51Zq6GjOnX44M

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: [email protected]