General Mathematics Quarter 2 – Module 1: Simple Interest and Compound Interest General Mathematics – Grade 11 Alternative Delivery Mode Quarter 2 – Module 1: Simple Interest and Compound Interest First Edition, 2020 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. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio SENIOR HS MODULE DEVELOPMENT TEAM Author Co-Author - Content Editor Co-Author - Language Reviewer Co-Author - Illustrator Co-Author - Layout Artist : Liza B. Bantay : Ma. Lourdes L. Agkis : Efren M. Bacani : Noel S. Sarili : Cherryl D. Cordova Team Leaders: School Head : Omar G. Magcalas LRMDS Coordinator : Cherryl D. Cordova DIVISION MANAGEMENT TEAM: Schools Division Superintendent OIC- Asst. Schools Division Superintendent Chief Education Supervisor, CID Education Program Supervisor, LRMDS Education Program Supervisor, AP/ADM Education Program Supervisor, Mathematics Project Development Officer II, LRMDS Division Librarian II, LRMDS : Romeo M. Alip, PhD, CESO V : William Roderick R. Fallorin, CESE : Milagros M. Peñaflor, PhD : Edgar E. Garcia, MITE : Romeo M. Layug : Danilo C. Caysido : Joan T. Briz : Rosita P. Serrano Printed in the Philippines by Department of Education – Schools Division of Bataan Office Address: Provincial Capitol Compound, Balanga City, Bataan Telefax: (047) 237-2102 E-mail Address: bataan@deped.gov.ph General Mathematics Quarter 2 – Module 1: Simple Interest and Compound Interest 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: Notes to the Teacher This contains helpful tips or strategies that will help you in guiding the learners. 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. 1 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. 2 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: References This is a list of all sources used in developing this module. 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! 3 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 4 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. 5 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 6 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/ 7 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 8 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 ______________________ ___________ __________________ 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% 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 9 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) ___________ __________________ ___________ __________________ 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. 10 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 July 26, 2019 = APPROXIMATE TIME 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 11 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 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 E 12 B. Complete the table. SIMPLE INTEREST P r t 15, 000 5% 1 Solution Interest Future Value Interest Future Value COMPOUND INTEREST P r t 15, 000 5% 1 Solution C. Find the actual time and approximate time from August 25, 2019 to April 11, 2020. 13 What I Have Learned Using Venn Diagram below, give the similarities and differences between simple interest and compound interest. SIMPLE INTEREST COMPOUND INTEREST 14 What I Can Do Accomplish a reflection journal using the given images below. 15 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. 16 Additional Activities Match each set of triangles to form a logical computation of a bigger triangle that includes the Principal, Time, Rate, and Interest. Principal 37, 500.00 Principal 15,000.00 Principal 12,000.00 Time 2.5 years Time 9 months Time 5 years Rate 5.3% Interest 6, 093.75 Rate 6.5% Interest 2, 250.00 17 Rate 3% Interest 477.00