SIMPLE-INTEREST-AND-COMPOUND-INTEREST.pptx

About Simple interest and Compound Interest in Business Finance

1. SIMPLE INTEREST AND COMPOUND INTEREST

2. LEARNING OBJECTIVES: At the end of the lesson, the learners are expected to 1. illustrate simple and compound interest 2. distinguishe between simple and compound interest 3. evaluate simple and compound interest

3. One day, the Master was going on a trip and decided to entrust his wealth to three of his most trusted servants. The wealth shall be given to each servant based on the Master’s assessment of their talents.

4. To his first servant, he entrusted P500,000. To his second servant, believing that he can make wise choices as well, he also gave an amount of P500,000.

5. Finally, he called on his third servant and gave him P500,000. The Master then went on his journey and told the servants he will not be back for a long time.

6. Since the 1st servant was a very smart person, he decided to invest the P500,000 given to him. He was very pleased that he was quoted a long-term investment for 5 years at 8% per annum compounded annually ,

7. and decided to invest the money on that institution. The second servant saw what the 1st servant did and also decided to invest the money.

8. However, when given the choice by the investment firm, he did not understand simple and compound interest. In the end, he accepted the quote at 8% per annum simple interest.

9. The 3rd servant saw them and thought that they were being too much of a risk-taker and decided to keep the money locked in a vault in his home.

10. The Master returned after 5 years. He then called on the servants and asked them what has become of the wealth he had entrusted them. (Parable of the Talents)

11. Definition of Terms Lender or Creditor - person (or institution) who invests the money or makes the funds available Borrower or debtor - person (or institution) who owes the money or avails of the funds from the lender Origin or loan date - date on which money is received by the borrower Repayment date or maturity date – a date on which the money borrowed or loan is to be completely repaid

12. Time or term (t) - amount of time in years the money is borrowed or invested; length of time between the origin and maturity dates Principal (P) - amount of money borrowed or invested on the origin date Rate (r) - annual rate, usually in percent, charged by the lender, or rate of increase of the investment Interest (I) - amount paid or earned for the use of money

13. Simple Interest (Is) - interest that is computed on the principal and then added to it. (Is = Prt) Maturity value or future value (F) - amount after t years; that the lender receives from the borrower on the maturity date Compound Interest (Ic) - interest is computed on the principal and also on the accumulated past interests. (Ic = F-P )

14. If an amount P is invested at an interest rate r compounded annually, then the investment will increase to a value A ( future value ), at the end of t years. It is modeled by the equation. ( 𝑨 = 𝑷(𝟏 + 𝒓)𝒕) Conversion period (m) – the number of times in a year the interest will be compounded, i.e., annually (m=1), semi-annually(m=2), quarterly(m=4) and monthly (m=12).

15. Servant 1 Servant 2 Servant 3 Principal P500,000.00 P500,000 P500,000 Interest 234,664.04 200,000 Total P734,664.04 P700,000 P500,000

16. Simple Interest Levied only on the loan amount or principal Principal never changes with increased tenure Easy to calculate using the formula Is = Prt FV = P+Is PV =   Compound Interest Levied on the loan amount as well as its interest Principal increases as interest compounds and gets added to it Difficult to calculate using the formula Ic = F-P or FV = 𝑷(𝟏 +  

17. ILLUSTRATIVE EXAMPLE Audly wants to deposit her P1000 money in a savings account. There are two banks that offer 6% interest per year. Compute for the balance of the deposit after 10 years if Audly deposit it in Bank A offering simple interest, or Bank B offering compounded interest.

18. SIMPLE INTEREST t Principal Yearly Interest Balance 1 1000 60 1060 2 1000 60 1120 3 1000 60 1180 4 1000 60 1240 5 1000 60 1300 6 1000 60 1360 7 1000 60 1420 8 1000 60 1480 9 10 1000 1000 60 60 1540 1600

19. COMPOUND INTEREST t Principal Yearly Interest Balance 1 1000 60 1060 2 1060 63.60 1123.60 3 1123.6 67.42 1191.02 4 1191.02 71.46 1262.48 5 6 7 8 9 10 Formula: A =   Formula: A = PxR

20. Problem 2 You won P10,000 and you plan to invest it for 10 years. A cooperative group offers 2% simple interest rate per year. A bank offers 2% compounded annually. Which will you choose and why?

21. Investment 1 - SIMPLE INTEREST t Principal Rate Simple interest Amount Solution Answer 1 10000 2% (10,000x2%x1) 200 10200 2 10000 2% (10,000x2%x2) 400 10400 3 10000 2% (10,000x2%x3) 600 10600 4 10000 2% 5 10000 2% 6 10000 2% 7 10000 2% 8 10000 2% 9 10000 2% 10 10000 2% 12000

22. Investment 2 - COMPOUND INTEREST t Principal Rate Simple interest Amount Solution Answer 1 10000 2% (10,000x2%) 200 10200 2 10200 2% (10,200x2%) 204 10404 (10000x 3 10404 2% (10,404x2%) 208.08 10612.08 4 2% 5 2% 6 2% 7 2% 8 2% 9 2% 10 2% 12189.94 t Principal Rate Simple interest Amount Solution Answer 1 10000 2% (10,000x2%) 200 10200 2 10200 2% (10,200x2%) 204 3 10404 2% (10,404x2%) 208.08 10612.08 4 2% 5 2% 6 2% 7 2% 8 2% 9 2% 10 2% 12189.94

23. The interest on a loan of Php 20,000.00 is Php 3,200.00. If the rate is 8%, when is the loan due? Given: P = Php 20,000.00 r = 8 % or .08 I = Php 3,200.00 t = I/Pr = Php 3,200.00/Php 20,000.00 (.08) = 2 years

24. Determine the simple interest rate if an investment of Php 25,000.00 accumulates Php 27,625.00 in 18 months. Given: P = Php 25,000.00 FV = Php 27,625.00 t = 18 months = 1.5 years I = FV – P = Php 27,625.00 – Php 25,000.00 = Php 2,625.00 r = I / Pt = Php 2,625.00 / Php 25,000.00(1.5) = .07 or 7 %

25. You invested Php 20,000.00 for three years at 5% compound interest rate. How much will you get after three years? P = Php 20,000.00 r = 5 % or .05 t = 3 years FV = Php 20,000 (1+.05)3 = Php 20,000.00 (1.05)3 = Php 23,152.50

26. EXERCISES SIMPLE INTEREST

27. 1. A bank offers 0.25% annual simple interest rate for a particular deposit. How much interest will be earned if P1,000,000.00 is deposited in this savings account for 1 year? Given: P= P1,000,000.00 r=0.25% or 0.0025 t=1 year

28. Solution: =Prt = P1,000,000 (0.0025)(1) = P2,500.00 Therefore, the interest that will be earned if P1,000,000 is deposited for 1 year at 0.25% is P2,500.00.  

29. 2. How much interest is charged if P50,000.00 is borrowed for 9 months at an annual interest rate of 10%? Given: P= P50,000.00 r=10% or 0.10 t=9 months

30. Solution: =Prt = P50,000 (0.10)(9/12) = P3,750.00 Therefore, the interest that will be earned if P50,000 is deposited for 9 months at 10% is P3,750.00.  

31. 3. When invested at an annual interest rate of 7%, the amount earned P11,200.00 of simple interest in 2 years. How much money was originally invested? Given: Is = P11,200.00 r=7% or 0.07 t= 2 years

32. Solution: = = P80,000.00 Therefore, the principal amount that should be investesd to earn P11,200 interest in 2 years at 7% is P80,000.00.  

33. SEATWORK: Solve the following exercises. 1. If an entrepreneur applies for a loan amounting to P500,000.00 in a bank, the simple interest of which is P157,500.00 for 3 years, what is the interest rate being charged?

34. 2. How long will a principal earn an interest equal to half of it at 5% simple interest?

35. 3. Find the maturity value of P1,000,000 if deposited in a bank at an annual simple interest rate of 0.25% after a. 1 year b. 5 years

36. 4. What are the amounts of interest and maturity value of a loan for P25,000 at 12% simple interest for 5 years?

37. 5. How much money will you have after 4 years and 3 months if you deposited P10,000.00 in a bank that pays 0.5% simple interest?

38. Group Activity: 1. How long will P1,000,000.00 earn a simple interest of P100,000.00 at 1% per annum?

39. 2. How much should you invest at the simple interest of 7.5% in order to have P300,000.00 in 2 years?

40. 3. What is the simple interest on a loan of P65,000.00 if the loan is given at a rate of 20% per annum and is due in 3 years?

41. 4. Miko borrowed P25,000.00 at 6.5% annual simple interest rate. How much should he pay after 3 years and 6 months?

42. 5. How much should you invest at 6% annual interest rate to obtain a simple interest of P72,000.00 in 3 years?

43. The Freedom of Taking Risk To laugh is to risk appearing a fool, To weep is to risk appearing sentimental, To reach out to another is to risk involvement, To expose feelings is to risk exposing your true self. To place your ideas and dreams before a crowd is to risk their loss. To love is to risk not being loved in return, To live is to risk dying, To hope is to risk despair, To try is to risk failure, But risks must be taken because the greatest hazard in life is to risk nothing. He may avoid suffering and sorrow, But he cannot learn, feel, change, grow or live. Chained by his servitude he is a slave who has forfeited all freedom. Only a person who risks is free. ∼ Leo Buscaglia (Book: Living, Loving & Learning)

44. EXERCISES COMPOUND INTEREST

45. EXERCISE 1 Due to the recent typhoon that cross along the Bicol region, Dada a resident of the said province thinks of a business that can provide for her needs as well as the needs of her neighbors so she can be of help to others. Having no money at hand, she decided to borrow from a bank as the start -up capital of P50,000 at 7% interest rate compounded annually and payable within 5 years. Compute for the interest after 5 years.

46. 1. A bank offers 0.25% annual simple interest rate for a particular deposit. How much interest will be earned if P 1 million is deposited in this savings account for 1 year? EXERCISE 2

47. 2. Your father asks you about investment and wanted to know the interest that will be earned if he will invest P500,000 in a certain bank that offers an annual compounding interest of 8% in 5 years.What will you say to him? EXERCISE 2

48. 3. A local farmer wants to borrow money from Landbank of the Philippines to start the organic farming in his one(1) hectare agricultural land. The farmer needs P150,000.00 as start-up capital. The bank offers him 10% interest compounded annually. Compute for the total amount to be paid every year for 5 years. Show your answer in tabular form. EXERCISE 2

49. 1. A private school teacher plans to apply for a housing loan in the Home Mutual Development Fund or Pag-Ibig. It offers a loan amounting to P1,500,000.00, considering all the rules and regulations regarding the policy with 6.5% interest per annum payable within 15 years. EXERCISE 3

50. Compare the maturity value if interest will be paid using the simple interest and/or compound interest compounded yearly. Please use the model table to compute and compare the interest. EXERCISE 3

51. 2. You borrowed P10,000 from your classmate with an interest rate of 2% per month payable after 5months. How much is the total interest to be collected after 5months? How much is the total amount to be collected after 5 months? EXERCISE 3

52. 3. You borrowed P100,000 from China Bank with an interest rate of 5% compounded annually and payable after 5 years. a. How much is the total interest to be collected after 5 years? EXERCISE 3

53. 3.b. You invested the amount you borrowed in a non-bank institution offering 7.5% interest compounded annually. How much is your gain from your borrowing?

54. 4. Mr. Ocampo invested P150,000 at 10% compounded annually. He plans to get this amount after 6 years for his son’s college education. How much will he get?

55. 5.What is the interest of P25,000 if invested at 4.5% compounded annually in 3 years and 2 months?

56. 6. Mr. Bautista aims to have his investment grow to P500,000 in 4 years. How much should he invest in an account that pays 5% compounded annually?

57. 7. Peter borrowed P100,000 at 8% compounded annually? How much will he be paying after 2 years?

58. 8. Mr. Versoza wants to compare simple and compound interests on a P350,000.00 investment for 3 years and 3 months. a. Find the interest if funds earn 6.5% interest compounded annually. b. Find the interest if funds earn 6.5% interest simple interest for 1 year. c. Find the difference between the two interests.

59. 9. A time deposit account in a bank yields 5.5% compound interest annually. Jason invested P450,000.00 for 4 years in this account. How much interest will she gain?

60. 10. In order to have P250,000.00 in 5 years, how much should you invest if the compound interest is 12%?

61. II. Complete the table below by finding the unknown. a. Principal (P) Rate (r) Time (t) Interest a) 2.5% 4 1,500 36,000 b) 1.5 4,860 250,000 0.5% c) 275 500,000 12.5% 10 d)

62. II. Complete the table below by finding the unknown. b. Principal (P) Rate (r) Time (t) Compound Interest (Ic) Maturity Value (FV) P6,000.00 8% 12 years 1) 2) 12,000.00 5.5% 6 years and 9 months 3) 4) 60,000.00 9.75% 10 months 5) 6) 7) 1% 6years 8) P25,000.00 9) 7.5% 4 years and 6 months 10) P400,000.00

63. QUIZ: Choose the letter of the best answer. Write your answer on a separate sheet of paper. 1. Which interest is computed on the principal and then added to it? a. Simple c. annuity due b. Compound d. ordinary annuity

64. 2. The simple interest formula is I = Prt . What does the t represent? a. principal c. interest b. time d. percent rate

65. 3. All of the following are used to find simple interest, except? a. principal c. time b. rate of interest d. future value

66. 4. It is the amount after t years that the lender will receive from the borrower. a. Future Value c. interest b. Present value d. principal

67. 5. Rate of interest must be converted into________ before substituting to the formula of finding the interest. a. fractions c. mixed numbers b. decimals d. percentage

68. 6. The principal in the formula I=Prt is a . the amount of money borrowed or deposited b. the percent interest for the year c. the amount taxed d. the amount the bank owes you for being their customer

69. 7. The interest from the previous year also earns interest. Which of the following describes the statement? a. simple c. rate b. compound d. time

70. 8. Variable P in simple interest formula when you are the creditor stands for? a. Original amount borrowed b. Original Amount invested c. Maturity Amount borrowed d. Maturity Amount invested

71. 9. The following statements are true EXCEPT a. The amount invested to a compound interest yields to greater maturity value than a simple interest. b. The amount borrowed from a simple interest yields a smaller value than a compound interest. c. The simple interest yields only from initial principal amount. d. The interest in a compound account yields interest only from initial principal amount.

72. 10. Compound interest is favorable to the following except a. investor of a retirement fund b. person who saves in bank c. investor of stocks d. borrower of a loan

73. 11. If an entrepreneur applies for a loan amounting to P500,000 in a bank, the simple interest of which is P157,500 for 3 years, what interest rate is being charged?

74. 12. When invested at an annual interest rate at 7%, the amount earned P11,200 of simple interest in two years. How much money was originally invested?

75. 13. What is the maturity value or future value of 1million pesos deposited in a bank at an annual simple interest rate of 0.25% after (a) 1 year? (b) 5 years?

76. 14. Suppose your father deposited in your bank account P10,000 at an annual interest rate of 0.5% compounded yearly when you graduate from kindergarten and did not get the amount until you finish Grade 12. How much will you have in your bank account after 12 years?

77. 15. How much money should a student place in a time deposit in a bank that pays 1.1% compounded annually so that he will have P200,000 after 6 years?

78. Solution (Exercise 1) Time (t) in years Principal Interest Amount 1 50,000.00 7% or 0.07= 3500 53,500.00 2 53,500.00 3,745.00 57,245.00 3 57,245.00 4,007.15 61,252.15 4 61,252.15 4,287.65 65,539.80 5 65,539.80 4,587.79 70,127.59

79. Solution (Exercise 2) Time (t) in years Principal Interest Amount 1 1,000,000.00 0.0025=2500 1,002,500.00

80. Solution (Exercise 3) Time (t) in years Principal Interest Amount 1 P500,000.00 0.08=40,000 540,000.00 2 540,000.00 0.08=43,200 583,200.00 3 583,200.00 0.08=46,656 629,856.00 4 629,856.00 0.08=50,388.48 680,244.48 5 680,244.48 0.08=54,419.56 734,664.04