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SENIOR

HIGH

SCHOOL

General

Mathematics

Quarter 4

Module

11

Business and Consumer Loans

(Amortization and Mortgage)

General Mathematics

Quarter 4 – Module 11: Business and Consumer Loan

First Edition, 2020

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Published by the Department of Education Division of Pasig City

Printed in the Philippines by the Department of Education – Division of Pasig City

Development Team of the Module

Writer: Jerymie R. Rodriguez

Editors: Nenet M. Peñaranda

Reviewers: Louela O. Dolotina

Illustrator:

Layout Artist:

Management Team: Ma. Evalou Concepcion A. Agustin

OIC-Schools Division Superintendent

Carolina T. Rivera, Ed. D.

Assistant Schools Division Superintendent

Victor M. Javena, Ed. D.

Chief - School Governance and Operations Division

Manual A. Laguerta, Ed.D.

Chief-Curriculum Implementation Division

Education Program Supervisors

1. Librada L. Agon, Ed. D., EPP/TLE 2. Liza A. Alvarez , Science 3. Bernard R. Balitao, Araling Panlipunan 4. Joselito E. Calios, English 5. Norlyn D. Conde, Ed. D., MAPEH 6. Wilma Q. Del Rosario, LRMS 7. Ma. Teresita E. Herrera, Ed. D., Filipino 8. Perlita M. Ignacio, Ph. D., ESP/SPED 9. Dulce O. Santos, Ed. D., Kinder/MTB 10. Teresita P. Tagulao, Ed. D., Mathematics

Introductory Message

For the facilitator:

Welcome to the General Mathematics for Senior High School Module on Solving

Problems on Business and Consumer Loans (Amortization and Mortgage)!

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

Schools Division Office of Pasig City headed by its Officer-In-Charge Schools Division

Superintendent, Ma. Evalou Concepcion A. Agustin in partnership with the Local

Government of Pasig through its mayor, Honorable Victor Ma. Regis N. Sotto.

The writers utilized the standards set by the K to 12 Curriculum using the Most

Essential Learning Competencies (MELC) while overcoming their personal, social,

and economic constraints in schooling.

This learning material hopes to engage the learners into guided and independent

learning activities at their own pace and time. Further, this also aims to help learners

acquire the needed 21st century skills especially the 5 Cs namely: Communication,

Collaboration, Creativity, Critical Thinking and Character 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. Moreover, 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.

For the learner:

Welcome to the General Mathematics Module on Business and Consumer Loans (

Amortization and Mortgage)

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 material while being an active learner.

This module has the following parts and corresponding icons:

Expectation - These are what you will be able to know after completing the

lessons in the module

Pre-test - This will measure your prior knowledge and the concepts to be

mastered throughout the lesson.

Recap - This section will measure what learnings and skills that you

understand from the previous lesson.

Lesson- This section will discuss the topic for this module.

Activities - This is a set of activities you will perform.

Wrap Up - This section summarizes the concepts and applications of the

lessons.

Valuing - this part will check the integration of values in the learning

competency.

Post-test - This will measure how much you have learned from the entire

module. Ito po ang parts ng module

LESSON

The gradual extinction of loan over a period of time by means of sequence of

regular or equal payments as to principal and interest due at the end of equal

intervals of time is known as amortization.

In paying a loan into a sequence of regular payments, it is very important to

both the lender and the borrower to construct amortization schedule, this will be

their guide and they will both see how much of each payment goes to the principal

amount and how much interest is being paid.

DEFINITION OF TERMS

Amortization Method – method oy paying a loan (principal and interest) on

installment basis, usually of equal amounts at regular intervals

Amortization Schedule - is a complete table of periodic loan payments, showing the

amount of principal and the amount of interest that comprise each payment until

the loan is paid off at the end of its term.

Mortgage – a loan secured by a collateral, that the borrower is obliged to pay at

specified terms ( Example 1 : Housing Loan: If a person wants to acquire a house and

lot and plans to use the bank to finance it, the title of the house will not be given to the

person, unless he will pay the bank in full with the interest)

Chattel Mortgage – a mortgage on a movable property (Example 2: Example of

property used could be a boat, jewelries, paper properties such as stocks, bonds or a

car title)

Collateral – assets used to secure the loan. It may be a real-estate or other

investments_. (In example 1, the house and lot is the collateral, that’s why the title of_

the house is not directly given to the borrower, unless he will pay the bank in full)

Outstanding Balance – any remaining debt at a specified time

The following are the formulas we will use in solving:

Regular Payment: Outstanding balance after the mth payment

𝑃𝑉 (𝑖)

1 −( 1 +𝑖)

−𝑛

𝑚𝑡ℎ

𝑅 [ 1 −

( 1 +𝑖

)

−(𝑛−𝑚)

]

𝑖

PROBLEM SOLVING:

Problem 1: Consumer Loan

Eva obtained a loan of Php 50,000 to start her LUGAW business. She has to repay

the loan by equal payments at the end of every six months for 3 years at 10% interest

compounded semi-annually. Answer the following.

A. Find the periodic or regular payment.

B. How much interest was paid on the 1

st

payment?

C. How much is repaid to the principal on the 1

st

payment?

D. How much is the outstanding balance after the 4

th

payment?

E. Construct the amortization schedule

Solution A: Regular or periodic payment

Given:

Present Value (PV) = Php 50,000.

Time ( t ) = 3 years

Rate of Interest ( r ) = 10% = 0.

Conversion Period (semi-annual) – ( K ) = 2

Number of Periodic payments ( n ) = K(t) = 2(3) = 6

Interest rate per conversion periods ( i ) =

𝑟

𝐾

1. 10

2

Regular or periodic payment ( R ) =?

Therefore, the regular or periodic payment at end of every six months is ₱ 𝟗, 𝟖𝟓𝟎. 𝟖𝟕.

Solution B: Interest paid on the 1

st

payment.

Given:

Present Value (PV) = Php 50,000.

Interest rate per conversion periods ( i ) = 0. 05

Interest paid on the 1

st

payment (I 1st

Therefore, the interest paid on the 1

st

payment is ₱𝟐, 𝟓𝟎𝟎. 𝟎𝟎

Solution C: Amount repaid to the principal on the 1

st

payment

Given:

Regular or periodic payment ( R ) = ₱𝟗, 𝟖𝟓𝟎. 𝟖𝟕

Interest paid on the 1

st

payment (I 1st

Amount repaid to the principal on the 1

st

payment (D 1st

Therefore, the amount repaid to the principal on the 1

st

payment is ₱ 7 , 350. 87.

Solution D: Outstanding balance after the 4

th

payment

Given:

Regular or periodic payment ( R ) = ₱𝟗, 𝟖𝟓𝟎. 𝟖𝟕

Interest rate per conversion periods ( i ) = 0. 05

Number of Periodic payments ( n ) = K(t) = 2(3) = 6

Total number of periodic payments paid (m) = 4

Outstanding balance after the 4

th

payment (PV 4th

T herefore, the outstanding balance after the 4

th

payment is ₱𝟏𝟖, 𝟑𝟏𝟔. 𝟖𝟏.

−𝑛

− 6

1 𝑠𝑡

1 𝑠𝑡

𝟏𝒔𝒕

1 𝑠𝑡

1 𝑠𝑡

1 𝑠𝑡

𝟏𝒔𝒕

4 𝑡ℎ

𝑅 [ 1 −

−

( 𝑛−𝑚

)

]

4 𝑡ℎ

9 , 850. 87 [ 1 − ( 1 + 0. 05 )

−( 6 − 4 )

𝟒𝒕𝒉

A. How much is the mortgage amount of the property?

Note: In this case the house itself is the mortgage property.

B. Find the periodic or regular payment?

C. How much interest was paid on the 1

st

payment?

D. How much is repaid to the principal on the 1

st

payment?

E. How much is the outstanding balance after the 5

th

payment?

F. Compute for the total of the regular payment, the interest component of

payment and the principal component of the payment.

Period

(n)

Regular

Payment

(R)

Interest

Component of

Payment

Principal Component

of Payment

Outstanding Balance

0 A.

1 B C D ₱2,053,731.

2 B ₱61,611.94 ₱202,156.70 ₱1,851,574.

3 B ₱55,547.24 ₱208,221.40 ₱1,643,353.

4 B ₱49,300.60 ₱214,468.04 ₱1,428,885.

5 B ₱42,866.56 ₱220,902.08 E

6 B ₱36,239.49 ₱227,529.15 ₱980,453.

7 B ₱29,413.62 ₱234355.02 ₱746,098.

8 B ₱22,382.97 ₱241,385.67 ₱504,713.

9 B ₱15,141.40 ₱248,627.24 ₱256,086.

10 B ₱7,682.58 ₱256,086.06 0

Total

F F F -

WRAP–UP

In this lesson, you were able to solve problems involving business loan and

consumer loan and you were able to create an amortization schedule which shows

the amount paid in each period. In your own words, what do you think is the

importance of creating an amortization schedule?

VALUING

The amortization schedule have taught us that, as the principal

amount reduces, the interest to be paid also decreases, and as the principal amount

get paid in greater amount, the interest will get smaller. Just like in life, it takes time

to succeed our dreams, but if we will pay a big amount of efforts into our dreams,

then we might have less burden in achieving it.

POSTTEST

Mr. Lime obtained a loan of Php 100,000.00 for the tuition fee of his children.

He has to repay the loan annually for 4 years with an interest rate of 10% per

annum. Answer the following questions.

1. What is the amount of annual amortization?

a. Php 31,457.08 c. Php 31,547.

b. Php 31,475.08 d. Php 31,754.

2. How much is the outstanding balance after the 2

nd

payment?

a. Php 54,751.13 c. Php 54,571.

b. Php 54, 715.13 d. Php 54,157.

3. How much interest was paid after the 3

rd

payment?

a. Php 5,574.11 c. Php 5,457.

b. Php 5,475.11 d. Php 5,547.

4. After the 3

rd

payment, how much is repaid to the principal amount?

a. Php 26,107.97 c. Php 26,170.

b. Php 26,701.97 d. Php 26,071.

5. How much interest will be paid for 4 years?

a. Php 26,188.32 c. Php 26,818.

b. Php 26,881.32 d. Php 26,188.