Solving Problems Involving Simple and Compound Interest: A General Mathematics Module, Study notes of Mathematics

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General Mathematics

Quarter 2 – Module 3:

Solving Problems Involving

Simple and Compound Interest

General Mathematics

Alternative Delivery Mode

Quarter 2 – Module 3 Solving Problems Involving Simple and Compound Interest

First Edition, 2020

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Development Team of the Module

Writers: Jerson D. Jolo

Editors: Elizabeth D. Lalunio, Elizabeth B. Dizon, Anicia J. Villaruel, Roy O. Natividad

Reviewers: Jerry Punongbayan, Necitas F. Constante, Fritz A. Caturay, Celestina M.

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iii

Introductory Message

For the facilitator:

Welcome to the General Mathematics Grade 11 Alternative Delivery Mode (ADM)

Module on Solving Problems Involving Simple and Compound Interest!

This module was collaboratively designed, developed and reviewed by educators from

public 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.

For the learner:

Welcome to the General Mathematics Grade 11 Alternative Delivery Mode (ADM)

Module on Solving Problems Involving Simple 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.

Notes to the Teacher

This contains helpful tips or strategies that

will help you in guiding the learners.

v

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.

Let’s find out how far you might already know about this topic by answering the

assessment below.

Choose the letter of the best answer. Write the chosen letter on a separate sheet

of paper.

For numbers 1- 5, use the situation below.

Michael borrowed money from Castañas Cooperative Bank at 1.75% simple

interest for 5 years to add to his funds for his new business. It was charged

₱ 5,250.00 for interest.

1. What formula will be used to determine the amount of borrowed money?

a. 𝐼

𝑠

b. 𝑃 =

𝐼

𝑠

𝑟𝑡

c. 𝐼

𝑐

𝑛

d. 𝑃 =

𝐹

( 1 +𝑟)

𝑡

2. How much money will Michael add on his funds for his new business?

a. ₱ 459.

b. ₱ 4 ,593.

c. ₱ 6 , 000.

d. ₱ 60,000.

3. How much will he need to pay after 5 years?

a. ₱ 5 ,709.

b. ₱ 9 ,843.

c. ₱ 11 , 250.

d. ₱ 65 , 250.

4. If Michael borrowed the same amount of money payable for the same

number of years and Castañas Cooperative Bank offered a promo as part

of its anniversary celebration and made all the interest loans 1.25%, how

much interest must be paid?

a. ₱ 3 , 750.

b. ₱ 37 , 500.

c. ₱ 63 , 750.

d. ₱ 70,000.

What I Know

5. How much will he need to pay after 6 years if he availed the promo?

a. ₱ 64,500.

b. ₱ 65,250.

c. ₱ 70,000.

d. ₱ 74,500.

For numbers 6 – 10 use the problem below.

Gerson Joseph has ₱ 300,000.00 to invest at 1.12% compounded quarterly.

6. What is the total number of compounding frequency if the investment

matures after 6 years?

a. 4

b. 6

c. 10

d. 24

7. How much is the interest rate per conversion period?

a. 1.12%

b. 0.19%

c. 0.28%

d. 0.05%

8. How much is the maturity value of his investment in 4 years?

a. ₱ 300,000.

b. ₱ 313,725.

c. ₱ 466,671.

d. ₱ 467,476.

9. How much is the compound interest after 4 years?

a. ₱ 3 , 000.

b. ₱ 13,725.

c. ₱ 16,671.

d. ₱ 16,746.

10. How much is the additional interest earned if instead of 4 years the

investment matures after 6 years?

a. ₱ 7 ,096.

b. ₱ 13 ,725.

c. ₱ 20 ,822.

d. ₱ 34,548.

Lesson

Solving Problems Involving

Simple Interest

One of the most common scenarios in our daily lives is engaging ourselves

in a business transaction. It is all but natural because many actions that we

undertake involve money. Moreover, when we are talking about money we usually

involve ourselves with the different problems that need solutions especially when

it comes to the computation of interest and the total amount to be paid at the end

of a particular term. So, are you ready to systematically solve problems involving

simple interest?

For you to begin, consider the previous lesson which is essential in this topic.

You already learned that in simple interest the basis of computation is the original

principal. There are also different formula to be used in finding the different

components in simple interest and these are the following:

𝑠

= 𝑃𝑟𝑡 ; simple interest

𝐹 = 𝑃( 1 + 𝑟𝑡) or = 𝑃 + 𝐼

𝑠

; maturity value

𝐼 𝑠

𝑟𝑡

; principal or present value

where:

P= principal or present value

F = maturity value

r= rate

t= time

I

s

= Simple Interest

What’s In

Let us consider the following examples:

1. Find I s

, if P = ₱ 4 , 500 .00, t= 3 and r = 2.

𝑠

𝑠

The simple interest is ₱ 337.

2. If P=₱ 3,375.00, r= 1.2% and t= 2 years find F

F= ₱ 3,456.

The maturity value is ₱ 3,456.

This or That

Febie is planning to invest her money in a bank. She researched some banks

which will make a better offer. She narrowed down her choices to these two banks

which have the following offers:

What’s New

Notes to the Teacher

Advise the learners to use scientific calculators because of the

nature of the numbers that will be computed. Remind them as well

that there are some formulas that will be used in this module that

has a different representation of variables in other books. Both will

yield the same answer as long as they represent the same

components.

covered by the Insurance Bank is shorter. If Febie will deposit on Insurance bank

her ₱5,000.00 savings will yield an interest of ₱ 225 .00 after 3 years. On the other

hand, if she choose to deposit her money in Trust Bank the interest that she will

earn is ₱ 525 .00 but this will only be realized after 6 years. The choice for the

bank where Febie will invest her money will depend upon her prerogative if she

wanted to have a long term investment she can choose Trust Bank but if she

thinks that she will need money in the near future she can invest in the Insurance

Bank. There are times that the amount of return is not the only factor to consider

in our choice since there are other components involved in the simple interest

formula and that is what we will explore in this lesson by solving problems

involving simple interest.

In solving problems involving simple interest, we can follow the 4 – step rule of

George Polya.

Let us take the following examples.

1. Mariel deposited ₱ 16,000.00 in a bank that offers a simple interest rate of

1.75%. If she placed the money for 7 years, how much interest will she

earn?

2. Janice has a loan with an interest rate of 1.5%. The amount of interest is

₱ 2,250.00 for a period of 3 years. How much is her loan?

In solving the problems, we will use the steps provided.

1. Mariel deposited ₱ 16,000.00 in a bank that offers a simple interest rate of

1.75%. If she placed the money for 7 years, how much interest will she

earn?

Explore. After reading and understanding the problem, it will be determined that

the required component is the simple interest and the following are the known

values:

What’s More

George Polya’s 4 – Step Rule

1. Explore. This step involves careful reading, analyzing, identifying the

given and unknown facts in the problem and expressing the unknown in

terms of variables.

2. Plan. In this step, writing an equation that describes the relationships

between or among the variables is involved.

3. Solve. This step requires working out with the written equation and other

number relations to determine the required quantities that answer the

question in the problem.

4. Check. The final step that employs the use of other approaches to

examine the appropriateness of the answer.

P = ₱ 16,000.

r = 1.75%

t= 7 years

Plan. Since the value of simple interest is required, the formula 𝐼 𝑠

= 𝑃𝑟𝑡 will be

applied.

Solve: Using the formula we will arrive at:

𝑠

𝑠

Check. As for checking, we can use other formulas related to simple interest and

substitute the value of simple interest. If the obtained value is any of the given

facts, then you obtain the correct answer.

Mariel earned ₱ 1,960.00 interest.

2. Janice has a loan with an interest rate of 1.5%. The amount of interest is

₱ 2,250.00 for a period of 3 years. How much is her loan?

Explore. The known values are

𝑠

r = 1.5% or 0.

t = 3 years

The required value is the Principal or present value

Plan. Since the problem requires the present value or the principal the formula

to be used is

𝑠

Solve: Using the formula, we will arrive at:

𝑠

Write a synthesis journal from the different activities and discussion you

encounterd from this module. You can recall past experiences and real life

problems and how you can solve and apply it in the future.

Synthesis Journal

What I did What I learned How I can use it

Making Money Happen

You are an investor who is aiming to accumulate a money amounting to

₱100,000.00 at the end of a specific year. Make plans of the amount to be

invested, terms and rate of investment for simple interest then choose which

between the plans is more realistic for a starting investor.

What I Have Learned

What I Can Do

2. Marinel received ₱ 1,450,500.00 as her inheritance from her

parents. She deposited the said amount in a time deposit with

1% interest rate per annum, how much money will be

accumulated after 7 years?

Components Plan 1 Plan 2

Present Value

Rate

Time

Simple Interest

Maturity Value

Plan Chosen:________________________________________________________

Reason for Choice:___________________________________________________

____________________________________________________

Rubrics for Scoring:

Categories Excellent

Fair

Poor

Decision Making Skills Excellent

decision

making skills

is fostered.

Fair

decision

making

skills is

fostered.

Poor

decision

making

skills is

fostered.

Planning The goal set is

achievable and

realistic.

The goal set is

hard to

achieve.

The goal set is not

achievable and not

realistic.

Accuracy of

Solution

The

computations

made are all

correct.

The

computations

made have

flaws.

There is no attempt in

making computation.