Chapter 4: The Simple Interest. SHMth1: General Mathematics. Accountancy, Business and Management (ABM) Mr. Migo M. Mendoza
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1 Chapter 4: The Simple Interest SHMth1: General Mathematics Accountancy, Business and Management (ABM) Mr. Migo M. Mendoza
2 Chapter 4: The Simple Interest Lecture 14: Basic Concepts on Simple Interest Lecture 15: Computing Simple Interest Problem Lecture 16: The Maturity Value and Present Value Lecture 17: Exact and Ordinary Interests Lecture 18: Time Between Two Dates
3 Lecture 14: Basic Concepts on Simple Interest SHMth1: General Mathematics Accountancy, Business and Management (ABM) Mr. Migo M. Mendoza
4 Classroom Task: Family Activity 2: Views about Interest Rates SSMth1: Precalculus Science and Technology, Engineering and Mathematics (STEM) Mr. Migo M. Mendoza
5 Instructions: Gather your family members and discuss the following views about interest rates. Please prepare a fiveminute presentation about it. The presentation can be in a form of a family report, skit etc.
6 Grading System: Criteria Percentage Content 40 Organization of Ideas 20 Communication Skills 15 Presentation and Aesthetic Consideration Behavior during the Presentation 15 10
7 Views about the Interest Rates The lower the interest rate the more people are over-optimistic to borrow money.
8 Views about the Interest Rates The higher the interest rate the lesser people are optimistic to borrow money.
9 Views about the Interest Rates High interest rate hurts seasonal businesses.
10 Views about the Interest Rates The government benefits from interest rates.
11 Views about the Interest Rates Businesses and foreign investors benefit from interest rates.
12 Something to think about Lender vs. Borrower
13 The Three (3) Categories of Interest 1. Simple Interest 2. Simple Discount 3. Compound Interest
14 The Simple Interest SHMth1: General Mathematics Accountancy, Business and Management (ABM) Mr. Migo M. Mendoza
15 The Simple Interest Simple Interest is calculated only on the original principal amount and is paid at the end of the loan period.
16 Take Note: Interest is calculated only on the original principal amount and is paid at the end of the borrowed money.
17 Three (3) Components of the Simple Interest The Principal (P) The Rate of Interest (r) The Time (t)
18 Principal (P) The refers to the sum of money invested, deposited or borrowed. We will use P (majuscule letter P) to denote or represent the principal.
19 Rate of Interest (r) This refers to the percentage of the principal per year and is generally expressed in terms of percent. The rate of interest is usually represent by r (minuscule letter r).
20 Take Note: The rate of interest is the percentage of the principal that will be charged for specified period of time (e.g. daily, weekly, monthly, yearly, etc.).
21 Take Note: Before computing rate in percent must be expressed in decimal form.
22 Time (t) This refers to the length of time between the date the loan is made and the date the loan becomes payable to the lender. To denote time we will use t (miniscule letter t).
23 Take Note: Time is usually expressed in years. When t is given in months, then the number months is divided by 12.
24 Lecture 15: Computing Simple Interest Problems SHMth1: General Mathematics Accountancy, Business and Management (ABM) Mr. Migo M. Mendoza
25 Learning Expectation: In this section we shall deal with the computation of simple interest.
26 Formula 1: The Amount of Simple Interest I Prt
27 Formula 1: The Amount of Simple Interest This shall be used in computing the amount of interest when principal amount (P), rate of interest (r), and the duration of the term (t) are given.
28 Take Note: In simple interest, the amount of interest earned per annum is constant.
29 Explanation: If the interest (I) for the first year is P100.00, then the value of I for the succeeding years shall also be P100.00, assuming of course that the Principal (P) and the interest rate are also constant.
30 Example 68: What amount of interest will be charged on the loan of Ms. Bea Ky of P7, borrowed for 3 years at a simple interest rate of 12% per annum?
31 Final Answer: The principal will earn an interest of P2,
32 Example 69: Nimfa Bebe deposited P5, in a bank paying 6% simple interest for 5 years. Compute the: a) amount of interest per annum; and b) total amount of interest for the entire period.
33 Example 70: Miss. Honeygirl Pulut-pukyutan borrowed P5, in a bank charging 12% per annum for a period of 6 years and 6 months. How much interest will she pay at the end of the term?
34 Take Note: What should we do when rate or percentage of interest (r) is unknown?
35 Classroom Task : Derive the formula for finding the rate of interest.
36 Formula 2: The Rate of Interest r I Pt
37 Formula 2: The Rate of Interest This formula shall be used when computing for the rate of interest when amount of interest, principal amount, and time are given.
38 Example 71: The simple interest received over a period of 5 years and 3 months on a loan of P22, is P11, Compute the rate of interest.
39 Something to think about What should we do when duration of the loan/ time (t) is unknown?
40 Classroom Task : Derive the formula for finding the time.
41 Formula 3: The Duration of the Loan/ Time t I Pr
42 Formula 3: The Duration of the Loan/ Time This shall be used in computing the time given the principal, rate and the amount of interest.
43 Example 72: Lhady_ZsUpFlaDeeTa borrowed P5, from a bank charging 12% simple interest. If she paid the amount of interest equivalent to P1,200.00, for how long did she use the money?
44 Example 73: TrOuFHaNG_QOuLLheTsz paid an amount P13, for a loan P25, at 10.5% interest rate. Find the duration of the term?
45 Something to think about What should we do when Principal (P) is unknown?
46 Classroom Task : Derive the formula for finding the principal amount.
47 Formula 4: The Principal Amount P I rt
48 Formula 4: The Principal Amount This shall be used in computing the Principal when amount of interest, rate of interest and time are given.
49 Example 74: bhozss_mhapa6mahal paid an interest of P2, on a loan for 2 years at 9.5% interest rate. How much was the original loan?
50 Performance Task 13: Please download, print and answer the Let s Practice 13. Kindly work independently.
51 Lecture 16: The Maturity Value and the Present Value of the Simple Interest SHMth1: General Mathematics Accountancy, Business and Management (ABM) Mr. Migo M. Mendoza
52 The Maturity Value (F) This refers to the sum of money at the end of the period when a certain amount of money is deposited or borrowed.
53 The Maturity Value (F) Maturity Value denoted by F is also called as the accumulated value, future value, and final value.
54 The Maturity Value (F) In other words, maturity value is equal to the sum of the amount of principal and the amount of interest.
55 Classroom Task : Derive the formula for finding the maturity value (F).
56 Formula 6: The Maturity Value (F) F P( 1 rt)
57 Formula 6: The Maturity Value (F) This shall be used in computing the maturity value given the amount of principal and the amount of interest. Also, it can be computed when original loan, rate of interest and time are given.
58 Example 75: Miss Bea Bunda deposited an amount of P12, in a savings bank that gives 6.5% simple interest for 8 years. How much would she have in her account at the end of 8 years assuming that no withdrawals were made?
59 Example 76: Mr. Hagardo Versoza paid an interest of P5, on a loan for 3 years at 8% simple interest. Compute the value of: a) the original loan; and b) the amount Mr. Versosa paid at the end of 3 years.
60 Something to think about Based on our previous example, what is now the present value?
61 The Present Value (P) The present value is the current worth of future sum of invested, borrowed, or deposited money given a specified rate of return.
62 The Present Value (P) Since the present value is actually the principal, we will denote it using majuscule letter P.
63 Classroom Task: Derive the formula for finding the present value (P).
64 Formula 6: The Present Value (P) F P ( 1 rt)
65 Formula 6: The Present Value (P) This shall be used in computing the present value given the maturity value, rate and time.
66 Example 77: Determine the present value of an investment which accumulated to P48, in 6 years at 6% simple interest.
67 Example 78: The maturity value paid on a loan is P72, If the loan was for 3 years at 9% simple interest, (a) how much was the original loan? (b) Compute the total amount of interest.
68 Something to think about Based on our previous example, what is the easiest way to compute the total amount of interest (I)?
69 Formula 7: The Total Interest I F P
70 Formula 7: The Total Interest (I) This shall be used in computing the total amount of interest given the maturity value and the present value.
71 Performance Task 14: Please download, print and answer the Let s Practice 14. Kindly work independently.
72 Lecture 17: The Exact and the Ordinary Interests SHMth1: General Mathematics Accountancy, Business and Management (ABM) Mr. Migo M. Mendoza
73 A Short Recap When the term of investment is expressed in days, what would be the approach in computing for the amount of interest?
74 The Two Approaches Two Approaches in Computing for the Amount of Interest Given the Time in Dates: 1. Exact Interest Method 2. Ordinary Interest Method
75 The Exact Interest This is used when interest is computed on the basis of 365 days a year or 366 days in a leap year.
76 The Exact Interest To denote Exact Interest we will use the symbol I e (majuscule letter I and subscript minuscule letter e).
77 Formula 8: The Exact Interest (I e ) Pr t Pr t I ori e 365 e 366
78 Formula 8: The Exact Interest This shall be used in computing for the exact interest, given the principal amount, the rate of interest and time per days.
79 The Ordinary Interest (I o ) This is used when interest is computed on the basis of an assumed 30- day/month or 360- day/year.
80 The Ordinary Interest (I o ) To denote Ordinary Interest we will use the symbol I o (majuscule letter I and subscript minuscule letter o).
81 Formula 9: The Ordinary Interest (I o ) I o Prt 360
82 Formula 9: The Ordinary Interest (I o ) This shall be used in computing for the ordinary interest, given the principal amount, the rate of interest and time per days.
83 Example 79: Mr. Benny Bilang invested an amount of P28, at 7% simple interest for 100 days. Compute the value of the: 1) exact interest; and 2) ordinary interest.
84 Example 80: Miss Lily Mangipin deposited an amount of P12, in a time deposit account at 8% simple interest for 150 days. Compute the value of the: exact interest; and the maturity value at the end of the term.
85 Performance Task 15: Please download, print and answer the Let s Practice 15. Kindly work independently.
86 Lecture 18: Time between Two Dates SHMth1: General Mathematics Accountancy, Business and Management (ABM) Mr. Migo M. Mendoza
87 Something to think about If two dates are given, how can we determine the number of days?
88 Example 81: Determine the number of days from September 21, 2017 to March 14, 2018.
89 Loan Date: This is the first day the loan/ deposit/ investment was made. It is also called as the origin date.
90 Hence, In our previous example the loan date or origin date is September 21, 2017.
91 Maturity Date This is the last day of the loan/ deposit/ investment. It is also called as the due date.
92 Hence, In our previous example the loan date or origin date is March 14, 2018.
93 Did you know? There are two ways in determining the number of days given two dates.
94 Two Ways in Determining Number of Days Given Two Dates Two Ways in Determining the Number of Days Given Two Dates: (1) Actual Time (2) Approximate Time
95 The Actual Time (A c ) This refers to the exact number of days between two dates. It is obtained by counting the actual number of days in each month within the period of the transaction except the loan date.
96 The Approximate Time (A p ) This refers to the assumption that each month has 30 days. The number of days is obtained therefore by counting each day of each month within the period of the transaction except the loan date.
97 Something to think about How can we determine which are 30-day month and which are not?
98 The Knuckle Months Method The knuckle and the space between them are consecutively given the names of the months, each knuckle corresponds to months with 31 days and each space corresponds to a short month.
99 The Knuckle Months Method
100 Example 81: Determine the number of days from September 21, 2017 to March 14, 2018 using actual and approximate time methods.
101 Did you know? There are certain steps to follow in order to determine the number of days when loan date and maturity date are given.
102 Steps in Determining the Number of Days Given Two Dates Step 1: Identify the number of days remaining in the first month excluding the loan date.
103 Steps in Determining the Number of Days Given Two Dates Step 2: Write the number of days in each succeeding month.
104 Steps in Determining the Number of Days Given Two Dates Step 3: Identify the number of days in the last month including the maturity date.
105 Steps in Determining the Number of Days Given Two Dates Step 4: Add the days from the first month to the last month.
106 Example 82: Determine the actual and approximate time from February 1, 2016 to December 25, 2016.
107 Did you know? When dealing with transactions where the loan and maturity dates are given, we have four possible ways of computing the period t.
108 Four Methods for Computing the Amount of Interest Given Two Dates Four Methods for Computing the Amount of Interest Given Two Dates: 1.Actual Time, Ordinary Interest Method 2.Actual Time, Exact Interest Method 3.Approximate Time, Ordinary Interest Method 4.Approximate Time, Exact Interest Method
109 Formula 10: Actual Time, Ordinary Interest Method I o Pr Ac 360
110 Formula 10: Actual Time, Ordinary Interest Method This shall be used in computing for the ordinary interest when amount of principal, rate of interest and actual time are given.
111 Formula 11: Actual Time, Exact Interest Method I e Pr A 365 c
112 Formula 10: Actual Time, Exact Interest Method This shall be used in computing for the exact interest when amount of principal, rate of interest and actual time are given.
113 Formula 12: Approximate Time, Ordinary Interest Method I o Pr A 360 p
114 Formula 12: Approximate Time, Ordinary Interest Method This shall be used in computing for the ordinary interest given the amount of principal, rate of interest and approximate time.
115 Formula 13: Approximate Time, Exact Interest Method I e Pr A 365 p
116 Example 83: An amount of P18, was invested to McDollibee at 8% simple interest on May 25, How much shall be the amount of interest earned on October 12, 2016 using the four methods of computing period t?
117 Banker s Rule: This is the common commercial practice and is the most favorable of all methods to the lender. This rule is an advocate of Actual Time, Ordinary Interest method.
118 Something to think about Why do you think most of the lenders or banks love to use banker s rule?
119 Did you know? Since ordinary interest is greater than exact interest and actual time is greater than approximate time. Actual time with ordinary interest method yields the highest amount. Therefore, more money! More profit! Yehey!
120 Example 84: On December 25, 2011, LIBING Things Funeral Parlor deposited an amount of P15, in a bank that pays 6.5% simple interest. Compute the maturity value on August 8, 2012, using the: 1) Banker s Rule; and 2) Approximate time, Exact Interest method.
121 Performance Task 16: Please download, print and answer the Let s Practice 16. Kindly work independently.
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