SHSGeneral MathematicsModule 34:Business Loans and Consumer LoansGeneral Mathematics Grade 11/12-Module 34: Business Loans and Consumer Loans First Edition, 2020 Show Copyright © 2020 La Union Schools Division Region I All rights reserved. No part of this module may be reproduced in any form without written permission from the copyright owners. Development Team of the Module Author: Raymart V. Gaco Editor: SDO La Union, Learning Resource Quality Assurance Team Illustrator: Ernesto F. Ramos Jr., P II Management Team: Atty. Donato D. Balderas, Jr. Schools Division Superintendent Vivian Luz S. Pagatpatan, Ph. Assistant Schools Division Superintendent German E. Flora, Ph., CID Chief Virgilio C. Boado, Ph., EPS in Charge of LRMS Erlinda M. Dela Peña, Ed., EPS in Charge of Mathematics Michael Jason D. Morales, PDO II Claire P. Toluyen, Librarian II TargetIn the previous lessons, you studied the concepts of interest and annuity. From there, you have learned how to compute interest, future and present values of annuities. In this section, you will be introduced to the concepts of loan and its types. Also, you will be equipped with the necessary skills in solving problems that involve these types of loans. After going through this learning material, you are expected to attain the learning objectives: Learning Competency: Illustrates business and consumer loan (M11GM – IIf – 1) Distinguishes between business and consumer loans (M11GM – IIf – 2) Solve problems involving business and consumer loans (amortization and mortgage) (M11GM – IIf – 3) Subtasks: Define loan Differentiate business and consumer loans Construct amortization schedule Before going on, check how much you know about this topic. Answer the pre-test on the next page in a separate sheet of paper. What I KnowPRE- TEST Before you proceed with this module, let’s assess what you already know about the lesson. Directions : Read and answer each question carefully. Write the letter of your answer on a separate sheet of paper.
For items 7 – 9, use the problem below. Phoebe obtained a loan amounting to P350,000 payable for 4 years. The monthly amortization is P8,709.
JumpstartThe basic concepts of loans are very familiar to every individual. Through loans, people, business persons, entrepreneurs, and even family persons receive assistance in addressing financial needs from different lending corporation. Loans are not just limited to borrowing money in a bank to finance business expansion, but also covers the use of credit card, amortizing appliances, and many more. ACTIVITY: Loan is the key! Directions : Read the given situation below and answer the questions that follow. Last September 27, 2009, Philippines was hit by typhoon Pepeng. Unluckily, the house of Mr. Duran was one of the many houses that was greatly devastated during the landfall. With no enough money on hand for his house renovation, he went to a bank and applied for a loan amounting to P400,000. The bank offered him an interest rate of 6% per annum which will be paid monthly for 3 years. On October 12, 2009, his loan was approved and right after, he started buying materials for his house renovation. Questions:
or a business loan? For you to understand the lesson well, do the following activities. Have fun and good luck! DiscoverFINANCIAL LOAN It is a form of debt contract entered into by two parties, an organization or an individual. The lender which is usually a financial institution advances a sum of money to the borrower. In return, the borrower agrees to certain set of terms which includes the principal amount, interest rate, finance charges, and other conditions. Loans can be classified as secured or unsecured loan. What is the difference between secured and unsecured loan? In a secured loan , the borrower pledges some assets as collateral for the loan. Collateral could be real-state or other investments. In case the borrower fails to pay his/her obligations, the lender has the right to take possession of the assets pledge by the borrower. On the other hand, an unsecured loan is a loan that is approved without the need for collateral. Loans also differ in form. The two most common types of loans are business and consumer loans. What is the difference between a consumer loan and business loan? A business loan is a money lent specifically for a business purpose. It may be used to start a business or to have a business expansion. On the other hand, a consumer loan is a money lent to an individual for personal or family purposes. The most popular examples of consumer loans are mortgages, home equity, and credit card. To further distinguish a consumer loan from a business loan, let’s have some examples. A. Mr. Pepito, a government employee, plans to make some renovations in their house. Since he does not have enough cash, he decided to borrow money from the bank to cover the expenses for his house renovation. B. Mr. Dulay was able to put up another branch of his restaurant. This was made possible because of an approved loan from a lending institution. C. In order to finance the education of her child, Mrs. Daliba borrowed some money from the bank. D. Mr. Biscocho and his family decided to go for a trip outside the country. In order to cover the expenses for the trip, he decided to apply for a loan. payment is done monthly then m = 12. c. 𝑛 = 𝑚𝑡 = 12 ( 15 12 ) = 15 d. R =? Step 2. Substitute the values in the formula. ####### 𝑹 = 𝑷 [𝟏−(𝟏+𝒋) −𝒏 𝒋 ] ####### 𝑹 = 𝟏𝟎𝟎,𝟎𝟎𝟎 [𝟏−(𝟏+𝟎.𝟎𝟎𝟕𝟓) −𝟏𝟓 𝟎.𝟎𝟎𝟕𝟓 ] ####### 𝑹 = 𝟏𝟎𝟎,𝟎𝟎𝟎 [𝟏−(𝟏.𝟎𝟎𝟕𝟓) −𝟏𝟓 𝟎.𝟎𝟎𝟕𝟓 ] ####### 𝑹 = 𝟏𝟎𝟎,𝟎𝟎𝟎 [𝟏−𝟎.𝟖𝟗𝟑𝟗𝟕𝟐𝟓𝟑𝟕𝟖𝟒𝟎.𝟎𝟎𝟕𝟓 ] ####### 𝑹 = 𝟏𝟎𝟎,𝟎𝟎𝟎 [𝟎.𝟏𝟎𝟔𝟎𝟐𝟕𝟒𝟔𝟐𝟏𝟔𝟎.𝟎𝟎𝟕𝟓 ] ####### 𝑹 = 𝟏𝟎𝟎,𝟎𝟎𝟎 𝟏𝟒.𝟏𝟑𝟔𝟗𝟗𝟒𝟗𝟓𝟒𝟕 ####### 𝑹 = 𝟕𝟎𝟕𝟑.𝟔𝟒 Therefore, the monthly payment is P7073. Example 2 : Ms. Dulay borrowed P1,250,000 at a fixed interest rate of 10% per annum to purchase a car. The loan is to be repaid quarterly for 20 years. a. How much is her quarterly mortgage payment? b. How much is the total amount of money accumulated for 20 years? c. Find the total interest that she will pay for the loan. Solution: Step 1. Identify the given in the problem. a. P = P1,250, b. 𝑗 =𝑚𝑟=0. 10 4 = 0. 025 Since interest rate is 10%, then r = 0. Also, since payment is done quarterly then m = 4. c. 𝑛 = 𝑚𝑡 = 4( 20 ) = 80 d. R =? Since the given time t is in months, we convert 15 months to years. Thus, t = 15/12. Step 2. Substitute the values in the formula. ####### 𝑹 = 𝑷 [𝟏−(𝟏+𝒋) −𝒏 𝒋 ] ####### 𝑹 = 𝟏, 𝟐𝟓𝟎,𝟎𝟎𝟎 [𝟏−(𝟏+𝟎.𝟎𝟐𝟓) −𝟖𝟎 𝟎. 𝟎𝟐𝟓 ] ####### 𝑹 = 𝟏, 𝟐𝟓𝟎,𝟎𝟎𝟎 [𝟏−(𝟏.𝟎𝟐𝟓) −𝟖𝟎 𝟎.𝟎𝟐𝟓 ] ####### 𝑹 = 𝟏, 𝟐𝟓𝟎,𝟎𝟎𝟎 [𝟏−𝟎.𝟏𝟑𝟖𝟕𝟎𝟒𝟓𝟔𝟗𝟕𝟒𝟎.𝟎𝟐𝟓 ] ####### 𝑹 = 𝟏, 𝟐𝟓𝟎,𝟎𝟎𝟎 [𝟎.𝟖𝟔𝟏𝟐𝟗𝟓𝟒𝟑𝟎𝟓𝟑𝟎.𝟎𝟐𝟓 ] ####### 𝑹 = 𝟏, 𝟐𝟓𝟎,𝟎𝟎𝟎 𝟑𝟒.𝟒𝟓𝟏𝟖𝟏𝟕𝟐𝟐𝟏𝟐𝟖 ####### 𝑹 = 𝟑𝟔,𝟐𝟖𝟐.𝟓𝟔 Therefore, the quarterly mortgage amount is P36,282. b. To find the total amount of money accumulated for 20 years, we multiply the quarterly mortgage and the total number of payments made. Thus, we have Total amount accumulated = R x n = P36,282(80) = P2,902,604. c. To find the total interest, we subtract the loan amount from the total amount accumulated. Thus, we have Total interest = Total amount accumulated – P = P2,902,604 - P1,250, = P1,652,604. Example 3 : An amortized loan amounting to P150,000 is charged with an interest rate of 7% per annum. If payments will be made semi – annually for 2 years, how much is the periodic payment? Construct the amortization schedule. Solution: Step 1. Identify the given in the problem. a. P = P150, b. 𝑗 =𝑚𝑟=0. 07 2 = 0. 035 Since interest rate is 7%, then r = 0. Also, since payment is done semi - annually then m = 2. c. 𝑛 = 𝑚𝑡 d. To compute the principal reduction, we subtract the regular payment to the interest. Thus, we have Principal reduction (1st payment) – Interest = P40837 – P5250 = P35587. e. To compute the outstanding balance, we subtract the beginning principal (1st payment) to the principal reduction payment. Thus, we have Beginning Principal (1st payment) – Principal reduction = P150,000 - P35587. = P114,412. The summary for the first payment is shown below. SECOND PAYMENT (ROW 2) a. For the second payment, the beginning principal is P114,412. b. The computed regular payment is worth P40,837. c. To compute for the interest for the second payment, we multiply the beginning principal (second payment) by the interest rate per period. Thus, we have Interest (2nd payment) = P114,412 (0) = P4,004. d. To compute the principal reduction, we subtract the regular payment to the interest. Thus, we have Principal reduction (2nd payment) – Interest = P40,837 – P4004 = P36,833. e. To compute the outstanding balance, we subtract the beginning principal (2nd payment) to the principal reduction payment. Thus, we have Beginning Principal (2nd payment) – Principal reduction = P114,412- P36,833. = P77,579. The summary for the second payment is shown below. For the third and fourth payments, we follow the same procedures which yield to: Payment Number n Beginning Principal Regular Payment R Interest Payment Principal Reduction Outstanding Balance 1 P150,000 P40837 P5250 P35587 P114,412. Payment Number n Beginning Principal Regular Payment R Interest Payment Principal Reduction Outstanding Balance 1 P150,000 P40,837 P5250 P35587 P114,412. 2 P114,412 P40,837 P4,004 P36,833 P77,579. Payment Number n Beginning Principal Regular Payment R Interest Payment Principal Reduction Outstanding Balance 1 P150,000 P40,837 P5250 P35587 P114,412. ExploreENRICHMENT ACTIVITY 1: Direction: Given the definition, jumble the letters to form the correct word.
O N C U M R E S L A N O
A R M O I T A Z N I O T 6**.** It is a type of secured loan secured by a collateral that the borrower is obliged to pay at specified terms. O M T R G G E A
individual. N N C A I L F I A O N L A
and the outstanding balance after each payment is made. A R M O I T A Z N I O T S H C E U L D E ASSESSMENT 1: Directions: Identify if the given situations below illustrate a consumer loan or a business loan. Write BL for business loan, and CL for consumer loan. Use a separate sheet of paper for your answer. 2 P114,412 P40,837 P4,004 P36,833 P77,579. 3 P77,579 P40,837 P2,715 P38,122 P39,456. 4 P39,456 P40,837 P1,380 P39,456 0 DeepenDirections: Analyze and solve the problem. Use a separate sheet of paper for your solution and be guided by the rubric shown below. A client is applying for a loan amounting to P400,000 in the bank where you are working. You explained to the client that the bank is charging 9% interest rate per annum and that payment is to be made monthly. The client asked you how much will the monthly payment be if the loan will last for a.) 2 years b.) 3 years c.) 4 years so that he will have an idea how much will be deducted from his salary. Your task is to compute and explain to the client the monthly amortization, the total amount accumulated and total interest to be paid after a.) 2 years b.) 3 years c.) 4 years. Which do you think would be a better choice for the client considering the repayment term (1, 2 or 3 years) and the monthly salary deduction? Explain why? Directions : Read and answer each question carefully. Write the letter of your answer on a separate sheet of paper.
For numbers 7 – 9, refer to the given problem below. Problem: Phoebe obtained a loan amounting to P80,000 payable for 3 years. The monthly amortization is P2,451. 7. What is the total number of payments made to pay the entire loan? A. 3 C. 12 B. 4 D. 36 8. How much is the total amount paid after 3 years? A. P88,269 C. P88,569. B. P88,769 D. P88,969. 9. How much is the total interest? A. P8,269 C. P8,569. B. P8,769 D. P8,969. For numbers 10 – 15, refer to the given problem below. Problem: Mr. Chavez obtained P6,000,000 mortgage to purchase a house. The mortgage will be repaid for 20 years at 8% per annum compounded semi - annually. 10. What is the total number of payments made to pay the entire loan? A. 20 C. 60 B. 40 D. 80 11. How much is the semi - annual payment? A. P303,140 C. P303,340. B. P303,240 D. P303,440. 12. How much is the total amount paid after 20 years? A. P12,125,637 C. P14,125,637. B. P13,125,637 D. P15,125,637. 13. How much is the total interest? A. P6,125,637 C. P6,325,637. B. P6,225,637 D. P6,425,637. 14. How much is the interest paid on the first payment? A. P140,000 C. P240, B. P340,000 D. P540, 15. How much is the outstanding balance after the first payment is made? A. P5,636,859 C. P5,025,637. B. P5,936,859 D. P5,205,637. - Test: Pre
Enrichment Activity 1:
le 9. Amortization Schedu6. Mortgage 3. Business Loan Assessment 1:
Enrichment Activity 2: Yearly Amortization: P56,116. Payment Number n Beginning Principal Regular Payment R Interest Payment Principal Reduction Outstanding Balance P102,883 P56,116 1 P6,173 P102,883 2 P52,940 3 Assessment 2: P98,763 b. P46,291 a. Amortization Schedule: b. Assessment 2: 0 3. P32,67 B. 1. P5,991 2. P136,220. Gauge:
Key AnswerWhat type of loan is given to individuals for personal or family purpose?Personal loans are loans that can cover a number of personal expenses. You can find personal loans through banks, credit unions, and online lenders. Personal loans can be secured, meaning you need collateral to borrow money, or unsecured, with no collateral needed.
What is the term coined as the time it takes to pay the entire loan?A loan term is the length of time it will take for a loan to be completely paid off when the borrower is making regular payments. The time it takes to eliminate the debt is a loan's term.
Which of the following is an example of a consumer loan?The most common types of consumer loans are – mortgage, auto loan, education loan, personal loan, refinance loan, and credit card.
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What do you call a money lent to an individual for personal or family purpose?
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