GRADES 1 to 12 School JRLMHS-SHS Grade Level GRADE 11

DAILY LESSON LOG

Teacher GLENN A. PARAS Learning Area GENERAL MATHEMATICS

Teaching Date November 4-5, 2024 Quarter SECOND

Objectives must be met over the week and connected to the curriculum standards. To meet the
objectives, necessary procedures must be followed and if needed, additional lessons, exercises and
remedial activities may be done for developing content knowledge and competencies. These are
I. OBJECTIVES assessed using Formative Assessment strategies. Valuing objectives support the learning of content
and competencies and enable children to find significance and joy in learning the lessons. Weekly
objectives shall be derived from the curriculum guides.
The learner demonstrates understanding of key concepts of simple and compound
A. Content Standards
interests, and simple and general annuities.
The learner is able to investigate, analyze and solve problems involving
B. Performance Standards simple and compound interests and simple and general annuities using appropriate
business and financial instruments.
Computes interest, maturity value, future value, and present value in simple interest and
compound interest environment. M11GM-IIa-b-1
Solves problems involving simple and compound interest. M11GM-IIa-b-2

Learning objectives:
C. Learning Competencies
a. Familiarize themselves with compound interest of more than once a year;
(Write the LC Code)/Objectives
b. Solve problems involving compound interest, present value and maturity value;
and,
c. Develop awareness in determining the compounding frequency, number of periods
and periodic rate.

Content is what the lesson is all about. It pertains to the subject matter that the teacher aims to
teach. In the CG, the content can be tackled in a week or two.
II. CONTENT Compound Interest (Compounding More Than Once a Year)

List the materials to be used in different days. Varied sources of materials sustain children’s interest
III. LEARNING RESOURCES in the lesson and in the learning. Ensure that there is a mix of concrete and manipulative materials
as well as paper-based materials. Hands-on learning promotes concept development.
A. References

1. Teacher’s Guide pages Curriculum Guide Mathematics Grade 7-12

2. Learner’s Material pages

3. Textbook pages General Mathematics, Orlando A. Oronce, pp. 196-200

4. Additional Materials from

Learning Resource portal

https://youtu.be/Usids2xsqoU
B. Other Learning Resources
https://youtu.be/Ws5kvWW1za8
These steps should be done across the week. Spread out the activities appropriately so that the
students will learn well. Always be guided by demonstration of learning by the students which you
can infer from formative assessment activities. Sustain learning systematically by providing
IV. PROCEDURES students with multiple ways to learn new things, practice their learning, question their learning
processes and draw conclusions about what they learned in relation to their life experiences and
previous knowledge. Indicate the time allotment for each step.
Answer the problem below.
A. Reviewing previous lesson or 1. What is compound interest?
presenting a new lesson (Elicit) 2.What does compounded annually means?

KNOW MY VALUE!
B. Establishing a purpose for the
Direction: Simplify the following.
lesson (Engage)
1. 34
 16
2.
4
2
3.(1+
6
)
12
Questions:
a. What principles did you used in solving the given problems?
b. Did you find it easy or difficult?

The teacher will show the table below.

Compounding Frequency Number of Periodic rate, i
Periods
Annually 1 i=annual interest rate
Semi- annually 2 i=annual interest rate÷ 2
Quarterly 4 i=annual interest rate÷ 4
C. Presenting examples/instances
of the new lesson (Explore)
Monthly 12 i=annual interest rate÷ 12
Daily 265 i=annual interest rate÷ 365

The students will ask to examine the table of values.

Questions:
1.What have you noticed in the table?
2. What are the equivalent period of each compounding frequency?

The teacher will discuss the following:

Compounding interest more than once a year is called “intra-year compounding”.

D. Discussing new concepts and
Interest may be compounded on semi-annual, quarterly, monthly, daily. When interest is
practicing new skills (explain #1)
compounded more than once a year, this affects the both future and present-value
calculations.

E. Discussing new concepts and CONTENT OF THE LESSON

practicing new skills (Explain
#2) COMPOUNDING MORE THAN ONCE A YEAR
Frequency of conversion (m)- number of conversion period in one yea.
Conversion of interest period- time between successive conversion of interest

Total number of conversion periods (n)

n=mt (frequency of conversion) x (time in years)
Nominal rate (Im) - annual rate of interest or interest rate per year.
m
i annual rate of interest
Rate-(j) of interest for each conversion period. J= =
m mfrequency of conversion
Frequency of conversion
Annually m=1
Semi-annually m=2
Quarterly m=4
Monthly m=12

Since the rate for each conversion period is presented by j, then in t years, interest is
compounded mt times. Thus, the formula of Maturity Value for interest Compounding m
times a year is:
MATURITY VALUE (F) AT COMPOUND INTEREST

r mt
F= P(1+ ) or F= P(1+i)n
m
Where :
F=maturity value
P= Principal value
r- nominal rate
m=frequency of convesion
n=mt
 r
i=
m

Example 1: Find the maturity value and interest if ₱10,000 is deposited in a bank at 2%
compounded quarterly for 5 years.
Given:
P=10,000 r=0.02 t= 5 years
r 0.02
i= = n=mt=(4)(5)= 20 conversion
m 4

Solution:
F= P(1+j)n
= (10,000)(1+0.005)20
= ₱11, 048.96
Compound Interest
IC=F-P
= 11,048.96-10,000
=₱1, 048.96

Example 2:
Find the maturity value and interest if ₱25,000 is deposited in a bank at 8% compounded
monthly for 5 years.

Given:
P=25,000 r=0.08 m=12

r 0.08
i= = = 0.0067 n=mt= (4)(5)= 20 conversion
m 12

Find Maturity value (F) IC=F-P

F=P(1+J)n = 28,553.13-25,000
=25,000 (1+0.0067) 20 =₱3,553.13
= ₱28,553.13
PRESENT VALUE (P) AT COMPOUND INTEREST

F
P= n
(1+i)

Where:
P- principal or present value
F- maturity (future) value at the end of the term.
r-nominal rate
t- term/ time in years
m- frequency of conversion

Example 1:
Find the present value of ₱50,000 due in 4 years if money is invested at 12%
compounded semi-annually.
Given: F=₱50,000 t= 4 r=0.12 m=12
r 0.12
i= = =0.08 n= mt= 12(4)=48
m 2

Solution:

F 50,000 50,000
P= n= 8= 8 = ₱31,370.62
(1+i) (1+0.06) (1.06)

Example 2:
What is the present value of ₱25,000 due in 2 years and 6 months if money is worth 10%
compounded quarterly?
 Given: F=₱50,000 t= 2 years and 6 months r=0.10 m=4
r 0.10
i= = =0.025 n= mt= 4(2 ½ )=10
m 4
Solution:
Find P:
F 25,000 25,000
P= n= 10 = 10 = ₱19,529
(1+i) (1+0.025) (1.025)

Board work:
Direction: Answer the following:
1. When money is compounded monthly, the frequency of conversion is__________.
Answer :12
2. If the interest rate per conversion is 12% and money is compounded monthly, the
F. Developing mastery (Leads nominal rate is_____________. Answer: 12%
to Formative Assessment) 3. When the term is 3 years and 6 months and money is compounded semi-annually,
(Elaborate) the total number of conversion periods is______________. Answer: 7
4. When the annual interest rate is 16% compounded quarterly, the interest rate in
conversion period is ___________. Answer: 4%
5. When the total number of conversion periods is 12 and the term is 6 years, the
money is compounded_______________. Answer: semi-annually.

Solve the following.

G. Finding practical 1. Find the maturity value and interest if ₱10,000 is deposited in a bank at 2%
applications of concepts and compound monthly for 5 years. Answer: F= ₱11,050.79 Ic= ₱1,050.793.
skills in daily living 2. If F=₱18,000 with the rate of 3 % compounded quarterly for 6 years, find the present
(Elaborate/Extend) value and compound interest. P= ₱15,044.97 Ic= ₱2,955.04

The teacher will ask the students to answer the following questions.
H. Making generalizations and 1. What are the different conversion frequency used in solving compound interest
abstractions about the lesson of more than once a year?
(Explain/Elaborate) 2. How will you identify whether a given problem involves simple interest or
compound interest?
Seatwork
Direction: Answer the following.
1. Find the compound interest and maturity value if ₱ 32,000 with a rate of 5.5% is
compounded semi-annually for 10 years.
I. Evaluating learning
(Evaluation) 2. Cris borrows ₱50,000 and promise to pay the principal and interest at 12%
compounded money. How much must he repay after 6 years?
3. Robert puts ₱ 100,000 in a savings account paying 8% compounded monthly. At this
rate, how much money will be in the account after 4 years?

Assignment:
J. Additional activities for
Direction: On your notebook, answer the following questions.
application or remediation
1.What is simple annuity?
(Extend)
2. What are the different types of annuity? Define each.

V.REMARKS
Reflect on your teaching and assess yourself as a teacher. Think about your students’
progress this week. What works? What else needs to be done to help the students learn?
VI. REFLECTION Identify what help your instructional supervisors can provide for you so when you meet
them, you can ask relevant questions.
A. No. of learners who earned
80% on the formative
assessment
B. No. of learners who require
additional activities for
remediation
 C. Did the remedial lessons
work? No. of students who
caught up with the lesson
D. No. of learners who
continue to require
remediation
E. Which of the teaching
strategies work well? Why did
these work?
F. What difficulties did I
encounter which my principal
or supervisor help me solve?
G. What innovation or
localized materials did I
use/discover which I wish to
share with other teachers?

Prepared by: Checked by:

GLENN A. PARAS ENGR. JUDD EDWARD Z. HERNANDEZ, EdD
Teacher I Master Teacher I

Noted by: Approved:

Lourdes P. Eyo, PhD NOIME O. VILLEGAS
SHS OIC-Assistant Principal II School Principal II
GRADES 1 to 12 School JRLMHS-SHS Grade Level GRADE 11
DAILY LESSON LOG
Teacher GLENN A. PARAS Learning Area GENERAL MATHEMATICS

Teaching Date November 6, 2024 Quarter SECOND

Objectives must be met over the week and connected to the curriculum standards. To meet the
objectives, necessary procedures must be followed and if needed, additional lessons, exercises and
remedial activities may be done for developing content knowledge and competencies. These are
I. OBJECTIVES assessed using Formative Assessment strategies. Valuing objectives support the learning of content
and competencies and enable children to find significance and joy in learning the lessons. Weekly
objectives shall be derived from the curriculum guides.
The learner demonstrates understanding of key concepts of simple and compound
A. Content Standards
interests, and simple and general annuities.
The learner is able to investigate, analyze and solve problems involving
B. Performance Standards simple and compound interests and simple and general annuities using appropriate
business and financial instruments.
Illustrates simple and compound interests. M11GM-IIa-1
Distinguishes between simple and compound interest. M11GM-IIa-2
Computes interest, maturity value, future value, and present value in simple interest and
C. Learning Competencies compound interest environment. M11GM-IIa-b-1
(Write the LC Code)/Objectives Solves problems involving simple and compound interest. M11GM-IIa-b-2

Learning Objective/s
a. Evaluate Students Learning about Simple and Compound Interest
Content is what the lesson is all about. It pertains to the subject matter that the teacher aims to
teach. In the CG, the content can be tackled in a week or two.
II. CONTENT
Quiz
List the materials to be used in different days. Varied sources of materials sustain children’s interest
III. LEARNING RESOURCES in the lesson and in the learning. Ensure that there is a mix of concrete and manipulative materials
as well as paper-based materials. Hands-on learning promotes concept development.
A. References

1. Teacher’s Guide pages Curriculum Guide Mathematics Grade 7-12

2. Learner’s Material pages

 3. Textbook pages
4. Additional Materials from
Learning Resource portal
B. Other Learning Resources
These steps should be done across the week. Spread out the activities appropriately so that the
students will learn well. Always be guided by demonstration of learning by the students which you
can infer from formative assessment activities. Sustain learning systematically by providing
IV. PROCEDURES students with multiple ways to learn new things, practice their learning, question their learning
processes and draw conclusions about what they learned in relation to their life experiences and
previous knowledge. Indicate the time allotment for each step.
A. Reviewing previous lesson or
presenting a new lesson (Elicit)
B. Establishing a purpose for the
lesson (Engage)
C. Presenting examples/instances The teacher will explain the instructions of the Quiz.
of the new lesson (Explore)

D. Discussing new concepts and The teacher will discuss the importance of PEMDAS and Laws of exponents in solving
practicing new skills (explain #1) problems involving simple and Compound interest

E. Discussing new concepts and

practicing new skills (Explain #2)
F. Developing mastery (Leads to
Formative Assessment)
(Elaborate)
G. Finding practical
applications of concepts and
skills in daily living
(Elaborate/Extend)
H. Making generalizations and
abstractions about the lesson
(Explain/Elaborate)
Quiz
I. Evaluating learning I. Direction: Read the following statements carefully and choose the letter of the correct
(Evaluation) answer.
II.Direction: Solve the following problems. (Show your complete solution)
Assignment:
J. Additional activities for
Direction: Answer the following questions.
application or remediation
1. What is an annuity?
(Extend)
2. What are the different types of annuity?

V.REMARKS
Reflect on your teaching and assess yourself as a teacher. Think about your students’
progress this week. What works? What else needs to be done to help the students learn?
VI. REFLECTION Identify what help your instructional supervisors can provide for you so when you meet
them, you can ask relevant questions.
A. No. of learners who earned
80% on the formative
assessment
B. No. of learners who require
additional activities for
remediation
C. Did the remedial lessons
work? No. of students who
caught up with the lesson
D. No. of learners who
continue to require
remediation
 E. Which of the teaching
strategies work well? Why did
these work?
F. What difficulties did I
encounter which my principal
or supervisor help me solve?
G. What innovation or
localized materials did I
use/discover which I wish to
share with other teachers?

Prepared by: Checked by:

GLENN A. PARAS ENGR. JUDD EDWARD Z. HERNANDEZ, EdD
Teacher I Master Teacher I

Noted by: Approved:

Lourdes P. Eyo, PhD NOIME O. VILLEGAS
SHS OIC-Assistant Principal II School Principal II
GRADES 1 to 12 School JRLMHS-SHS Grade Level GRADE 11
DAILY LESSON LOG
Teacher GLENN A. PARAS Learning Area GENERAL MATHEMATICS

Teaching Date November 7-8, 2024 Quarter SECOND

Objectives must be met over the week and connected to the curriculum standards. To meet the
objectives, necessary procedures must be followed and if needed, additional lessons, exercises and
remedial activities may be done for developing content knowledge and competencies. These are
I. OBJECTIVES assessed using Formative Assessment strategies. Valuing objectives support the learning of content
and competencies and enable children to find significance and joy in learning the lessons. Weekly
objectives shall be derived from the curriculum guides.
The learner demonstrates understanding of key concepts of simple and compound
A. Content Standards
interests, and simple and general annuities.
The learner is able to investigate, analyze and solve problems involving
B. Performance Standards simple and compound interests and simple and general annuities using appropriate
business and financial instruments.
Illustrates simple and general annuities. M11GM-IIC-1
Distinguish between simple and general annuities. M11GM-IIC-2

C. Learning Competencies Learning Objective/s:

(Write the LC Code)/Objectives a. Define annuity payment;
b. Differentiate simple annuity from general annuity; and,
c. Solve problems involving future value of simple annuity.

Content is what the lesson is all about. It pertains to the subject matter that the teacher aims to
teach. In the CG, the content can be tackled in a week or two.
II. CONTENT
Future Value of Simple Annuity
List the materials to be used in different days. Varied sources of materials sustain children’s interest
III. LEARNING RESOURCES in the lesson and in the learning. Ensure that there is a mix of concrete and manipulative materials
as well as paper-based materials. Hands-on learning promotes concept development.
A. References

1. Teacher’s Guide pages Curriculum Guide Mathematics Grade 7-12

2. Learner’s Material pages

3. Textbook pages General Mathematics, Orlando A Oronce, pp. 203-226.
4. Additional Materials from
Learning Resource portal
B. Other Learning Resources https://youtu.be/hsj68ZST63g
These steps should be done across the week. Spread out the activities appropriately so that the
IV. PROCEDURES
 students will learn well. Always be guided by demonstration of learning by the students which you
can infer from formative assessment activities. Sustain learning systematically by providing
students with multiple ways to learn new things, practice their learning, question their learning
processes and draw conclusions about what they learned in relation to their life experiences and
previous knowledge. Indicate the time allotment for each step.
1. How to find the interest, present and future value of money or amount compounded
A. Reviewing previous lesson or annually?
presenting a new lesson (Elicit) 2. How can you identify that the given problem is compound interest?

The teacher will show the following terms and will let them examine what it means.
1. Rental payment
B. Establishing a purpose for the 2. Monthly pension
lesson (Engage) 3. Monthly payment for car loan
4. Educational plan

C. Presenting examples/instances The students will ask to differentate and give their insights on the given terms above.
of the new lesson (Explore) The teacher will discuss that the following are examples of annuities

Annuities may be classified in different ways, as follows.

ACCORDING TO PAYMENT INTERVAL AND INTEREST PERIOD

Simple annuity- an nnuity where the payment intervals is the same as the interest
period.
General Annuity- an annuity where the payment intervals is not the same as the interest
period.

ACCORDING TO TIME OF PAYMENT

Ordinary annuity- an annuity which payment are made at the end of of each payment
interval.
Contingent Annuity- an annuity which in the payment extend over an indefinite or
D. Discussing new concepts and
indeterminate ) length of time.
practicing new skills (explain #1)
ACCORDING TO DURATION
Annuity Certain- an annuity in which payments begin and end at definite times,

Contingent Annuity- an annuity in which the payment extend over an indefinite length of
time.

 Example of a simple annuity – installment payment for an appliance at the end of

each month with interest compounded monthly

 Example of a general annuity – installment payment for an appliance at the end

of each month with interest compounded annually

E. Discussing new concepts and Content of the Lesson

practicing new skills (Explain #2) Simple Annuity- the payment interval is also the same as the interest period.
General Annuity- refers to the annuity where the length of the payment interval is not
the same as the length of interest compounding period.

Each payment in the annity is called periodic payment.

Term of the annuity- it is the time between successive payment dates of annuity.
Future value- it is the sum of fuure values of all payments to be made dueing the entire
term of annuity
Present value- is the sum of the present values of all payments to be made during the
entire term of annuity.

Future Value of Simple Ordinary Annuity (F)

F = R ( 1 + j)n – 1
J
where R is the regular payment
 j is the interest rate per period, and
n is the number of payments

Example 1. Suppose Mrs. Remoto would like to save ₱3000 at the end of each month, for
six months, in a fund that gives 9% compounded monthly. How much is the future value
of her savings after 6 months?
Solution:
Given: R = ₱3000
term t = 6 months
interest rate per annum i(12) = 0.09
number of conversions per year m = 12
i 0.09
interest rate per period j = =¿ = 0.0075
m 12
1 year
n = m*t = (12 * 6months ( )) = 6
12months

Find: future value at the end of the term, F

F = R ( 1 + j)n – 1
j
= 3,000 ( 1 + 0.0075)6 – 1
0.0075
F = ₱18,340.89

Example 2. In order to save for her high school graduation, Marie decided to save ₱200
at the end of each month. If the bank pays 0.250% compounded monthly, how much will
her money be at the end of 6 years?

Solution:
Given: R = 200
t = 6 years
i(12) = 0.250% = 0.0025
m = 12
i 0.0025
j= =¿ = 0.0002083
m 12
n = m*t = (12*6) = 72 periods

Find: F
F = R ( 1 + j)n – 1
j
= 200 (1 + 0.0002083)72 – 1
0.0002083
F = ₱14,507.02

Directions: Fill in the blanks. Write your answer on a separate sheet of paper.
1. A sequence of payments made at equal time periods is a/an ____________
2. A simple annuity in which the payments are made at the end of each period is a/an
____________
F. Developing mastery (Leads to
3. An annuity where the payment interval is not the same as the interest period is a/an
Formative Assessment)
____________
(Elaborate)
4. An annuity where the payment interval is the same as the interest period is a/an
____________
5. An annuity in which payments begin and end at definite times is a/an ____________.

Dircetion: Answer the problembelow.

G. Finding practical
1. Payments are made at the end of each month for a loan that charges 1.05% interest
applications of concepts and
compounded quarterly.
skills in daily living
2. A deposit of ₱5,000was made at the endevery three months to a month that earns
(Elaborate/Extend)
5.6% interest compounded quarterly.
H. Making generalizations and 1. What are the different types of annuity?
abstractions about the lesson 2. Differentiate simple annuity from and general annuity.
 (Explain/Elaborate) 2. What are some considerations in solving the future value of simple annuity?
Directions: Find the future value of the following. Write your answer on a separate sheet
of paper.
1. Quarterly payments of ₱2,000 for 5 years with interest rate of 8% compounded
quarterly.
2. Semi-annual payments of ₱8,000 for 12 years with interest rate of 12% compounded
I. Evaluating learning semi-annually
(Evaluation) 3. Suppose Mrs. Remoto would like to save ₱3,000 every month in a fund that gives 9%
compounded monthly. How much is the amount or the future value of her savings after 6
months. Ans: 18,340.89
4. Peter started to deposit ₱5,000 quarterly in a fund that pays 1% compounded
quarterly. How much will be in the fund after 6 years?

Assignment:
J. Additional activities for
Direction: Answer the following questions.
application or remediation
1. Give real life examples of future value of simple annuity.
(Extend)
2. How to solve the present value of simple annuity?

V.REMARKS
Reflect on your teaching and assess yourself as a teacher. Think about your students’
progress this week. What works? What else needs to be done to help the students learn?
VI. REFLECTION Identify what help your instructional supervisors can provide for you so when you meet
them, you can ask relevant questions.
A. No. of learners who earned
80% on the formative
assessment
B. No. of learners who require
additional activities for
remediation
C. Did the remedial lessons
work? No. of students who
caught up with the lesson
D. No. of learners who
continue to require
remediation
E. Which of the teaching
strategies work well? Why did
these work?
F. What difficulties did I
encounter which my principal
or supervisor help me solve?
G. What innovation or
localized materials did I
use/discover which I wish to
share with other teachers?

Prepared by: Checked by:

GLENN A. PARAS ENGR. JUDD EDWARD Z. HERNANDEZ, EdD
Teacher I Master Teacher I

Noted by: Approved:

Lourdes P. Eyo, PhD NOIME O. VILLEGAS
SHS OIC-Assistant Principal II School Principal II