11

General Mathematics
Activity Sheets
Quarter 2 – MELC 6
Distinguishing Between Simple and
General Annuities

REGION VI – WESTERN VISAYAS

General Mathematics 11
Activity Sheet No. 06
First Edition, 2020

Published in the Philippines

By the Department of Education
Region 6 – Western Visayas

Republic Act 8293, section 176 states that: No copyright shall subsist in
any work of the Government of the Philippines. However, prior approval of the
government agency or office wherein the work is created shall be necessary for
exploitation of such work for profit. Such agency or office may, among other
things, impose as a condition the payment of royalties.

This Learning Activity Sheet is developed by DepEd Region 6 – Western

Visayas.

ALL RIGHTS RESERVED. No part of this learning resource may be

reproduced or transmitted in any form or by any means electronic or mechanical
without written permission from the DepEd Regional Office 6 – Western Visayas.

Development Team of General Mathematics Activity Sheet

Writer: Rutchel J. Ngipen

Illustrator: Rutchel J. Ngipen

Layout Artist: Rutchel J. Ngipen

Schools Division Quality Assurance Team:

Ligaya H. Montelijao, EPS-Mathematics
Leila G. Valencia, EPS-LR
Jezereel Grace G. Tiron
Bernie P. Alcedo
Division of Iloilo City Management Team:
Ma. Luz M. De los Reyes, SDS
Ernesto F. Servillon Jr., ASDS
Arlo L. Villalva, CID Chief
Dr. Jerry M. Lego, SGOD Chief
Leila G. Valencia, EPS-LR
Ligaya H. Montelijao, EPS-Mathematics
Regional Management Team
Ma. Gemma M. Ledesma,
Dr. Josilyn S. Solana,
Dr. Elena P. Gonzaga,
Mr. Donald T. Genine,
Mr. Adonis Mosquera
Mrs. Rhodalyn Delcano

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Introductory Message
Welcome to General Mathematics 11!

The Learning Activity Sheet is a product of the collaborative efforts of the

Schools Division of Iloilo City and DepEd Regional Office VI - Western Visayas
through the Curriculum and Learning Management Division (CLMD). This is
developed to guide the learning facilitators (teachers, parents and responsible
adults) in helping the learners meet the standards set by the K to 12 Basic
Education Curriculum.

The Learning Activity Sheet is self-directed instructional materials aimed

to guide the learners in accomplishing activities at their own pace and time using
the contextualized resources in the community. This will also assist the learners in
acquiring the lifelong learning skills, knowledge and attitudes for productivity and
employment.

For learning facilitator:

The General Mathematics Activity Sheet will help you facilitate the
teaching-learning activities specified in each Most Essential Learning Competency
(MELC) with minimal or no face-to-face encounter between you and learner. This
will be made available to the learners with the references/links to ease the
independent learning.

For the learner:

The General Mathematics Activity Sheet is developed to help you

continue learning even if you are not in school. This learning material provides you
with meaningful and engaging activities for independent learning. Being an active
learner, carefully read and understand the instructions then perform the activities
and answer the assessments. This will be returned to your facilitator on the agreed
schedule.

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 Quarter 2, Week 3

Learning Activity Sheets (LAS) No. 6

Name of Learner: ___________________ Grade and Section: _________________

Date: _____________________________

GENERAL MATHEMATICS ACTIVITY SHEET

Distinguishing Between Simple and General Annuities

I. Learning Competency with Code

Distinguishes between simple and general annuities. (M11GM-IIc-2)

II. Background Information for Learners

According to research, half of men reaching 65 can expect to live up to
age 85 or longer, and half of women reaching that age can expect to live
until 88 or longer. Thus, retirement often spans 20 years or more for men
and 23 years or more for women. In addition, longevity in other places
continues to increase. Yet, 69% of those who have savings and 92% of
those who don’t have savings believe that they will not have enough
money to live comfortably throughout retirement.
An annuity can be a guaranteed stream of payments that can provide
regular income for a certain period of years or a lifetime where anyone
nearing retirement or people desiring an income stream to cover specific
fixed expenses can be suited. The basic among annuities are simple
annuity and general annuity.
Take a look at the sample word problem for simple annuity and
compound annuity. Study the highlighted data in the problem.

Suppose Rodrigo, a high school annually

Payment Interval
student, would like to save ₱5,000
SIMPLE ANNUITY

annually in a fund that gives 10%

compounded annually. How much is
the amount or future value of his
savings after 4 years?
Interest Period annually

GENERAL ANNUITY
Suppose Rodrigo, a high
school student, change his
Payment Interval annually
mind and decided to save
₱5,000 annually in a fund that
gives 10% compounded semi-
annually. How much is the
amount or future value of his Semi-
Interest Period
savings after 4 years? annually

Observe again the sample cash flow time diagram on the next page for
simple annuity and compound annuity. Study the highlighted data in the
figure.

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 SIMPLE
P 0 ANNUITY1 2 3 F
4 years
1 year 1 year 1 year 1 year
₱5,000 ₱5,000 ₱5,000 ₱5,000

annually Payment Interval

Interest Period annually

GENERAL ANNUITY
P 0 1 2 3 F
4 years
6 months 6 mo. 6 months 6 mo. 6 months 6 mo. 6 months 6 mo.
₱5,000 ₱5,000 ₱5,000 ₱5,000

annually Payment Interval

Interest Period Semi-annually

Simple Annuity is an annuity where the payment interval is the same as

the interest period while General Annuity is an annuity where the
payment interval is not the same as the interest period

III. Accompanying DepEd Textbook and Education Sites

https://www.youtube.com/watch?v=rvlgY01iLlw
https://www.youtube.com/watch?v=Qr7qYrsOXgE
https://www.youtube.com/watch?v=iYghPrs7JtM
https://www.youtube.com/watch?v=Xt0kh8VGF-I
General Mathematics Learner's Materials. Pasig City: Department of
Education - Bureau of Learning Resources, 2016, pp 168-204

IV. Activity Proper

General Directions: In answering the exercises in the Learning Activity
Sheet (LAS), please be reminded not to write anything here. All answers
must be written in a separate sheet of paper. Read each problem carefully
and answer it systematically. If solution is required, encircle your final
answer.
Exercise 1: Read and understand each problem. Identify if the given
problem is simple annuity or general annuity.
1. You win a lottery and receive ₱50,000 every month at a rate of 0.2%
compounded every year.
2. Barry intends to borrow money as capital for his business. To pay it off
he will pay ₱10,000 at the end of every month for 5 years. The money
is compounded by 5% quarterly.
3. AJ, a promising pop star, plans to save money for the future. She will
set aside ₱5,000 at the end of every month and put it on an investment
company where her money will grow by 4.5% monthly. She will do this
for 20 years.

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 4. Art wants to earn his first million 15 years from now. To do this, he will
save money at the end of every 2 months and put it on an investment
company, where his money will grow by 6.4% semi – annually.
5. Helen started to join the barangay’s cooperative and agreed to
contribute ₱3,000 per month starting in January 2021, which will earn
4.1% compounded monthly.

Exercise 2: Given the following figures, do the following tasks:

a. Determine the payment interval.
b. Determine the interest period.
c. Distinguish whether the figure is simple annuity or general annuity.

1. P 0 F
1 2 3 4 5 6years
6 mo 6 mo 6 mo 6 mo 6 mo 6 mo 6 mo 6 mo 6 mo 6 mo 6 mo 6 mo
₱4,500 ₱4,500 ₱4,500 ₱4,500 ₱4,500 ₱4,500

2. P 0 1 2 3 4 F
5 6 years
1 year 1 year 1 year 1 year 1 year 1 year
₱4,000 ₱4,000 ₱4,000 ₱4,000 ₱4,000 ₱4,000

3. F
P 0 1 2 3 4 5 6months
1 month 1 month 1 month 1 month 1 month 1 month
₱6,000 ₱6,000 ₱6,000 ₱6,000 ₱6,000 ₱6,000

4. P 0 F
1 2 3 4 5 6quarterly
1 month 1 month 1 month 1 month 1 month 1 month
₱2,500 ₱2,500 ₱2,500 ₱2,500 ₱2,500 ₱2,500

Guide Question:
1. What data/clues do you need to look up to in the problem or figure for
you to be able to distinguish whether it is simple annuity or general
annuity?
2. How do you differentiate simple annuity from general annuity?

V. Reflection
Instruction. Reflect on the following questions and write your response on
your journal.
1. Why is distinguishing simple annuity and general annuity important in
your daily life or in the future?
2. If you are planning to invest or borrow, which annuity would you prefer
to follow? Why?

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VI. Answer Key

Exercise 1
1. General ; 2. General ; 3. Simple ; 4.General ; 5.Simple
Exercise 2
1. annually, semi-annually, general ; 2. annually, annually, simple ;
3. monthly, monthly, simple ; 4.quarterly, monthly, general