the simple interest · 2018-08-31 · the simple interest received over a period of 5 years and 3...
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Chapter 4:
The Simple InterestSHMth1: General Mathematics
Accountancy, Business and
Management (ABM)
Mr. Migo M. Mendoza
Chapter 4: The Simple InterestLecture 14: Basic Concepts on Simple InterestLecture 15: Computing Simple Interest ProblemLecture 16: The Maturity Value and Present ValueLecture 17: Exact and Ordinary InterestsLecture 18: Time Between Two Dates
Lecture 14: Basic Concepts on Simple Interest
SHMth1: General Mathematics
Accountancy, Business and
Management (ABM)
Mr. Migo M. Mendoza
Classroom Task:
Family Activity 2: Views about Interest Rates
SSMth1: Precalculus
Science and Technology, Engineering
and Mathematics (STEM)
Mr. Migo M. Mendoza
Instructions:Gather your family members and discuss the following views about
interest rates. Please prepare a five-
minute presentation about it. The
presentation can be in a form of a family report, skit etc.
Grading System:Criteria Percentage
Content 40
Organization of Ideas 20
Communication Skills 15
Presentation and Aesthetic Consideration
15
Behavior during the Presentation
10
Views about the Interest Rates…
The lower the interest
rate the more people are
over-optimistic to borrow
money.
Views about the Interest Rates…
The higher the interest
rate the lesser people are
optimistic to borrow
money.
Views about the Interest Rates…
High interest rate
hurts seasonal
businesses.
Views about the Interest Rates…
The government
benefits from interest
rates.
Views about the Interest Rates…
Businesses and foreign
investors benefit from
interest rates.
Something to think about…
Lender vs. Borrower
The Three (3) Categories of Interest
1. Simple Interest2. Simple Discount
3. Compound Interest
The Simple Interest
SHMth1: General Mathematics
Accountancy, Business and
Management (ABM)
Mr. Migo M. Mendoza
The Simple Interest
Simple Interest is calculated only on the original principal amount and is paid at the end
of the loan period.
Take Note:
Interest is calculated only on the original principal
amount and is paid at the end of the borrowed money.
Three (3) Components of the Simple Interest
The Principal (P)The Rate of Interest (r)
The Time (t)
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.
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).
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.).
Take Note:
Before computing rate in percent must be expressed
in decimal form.
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).
Take Note:
Time is usually expressed in years. When t is given in months, then the number months is divided by 12.
Lecture 15: Computing Simple Interest Problems
SHMth1: General Mathematics
Accountancy, Business and
Management (ABM)
Mr. Migo M. Mendoza
Learning Expectation:
In this section we shall deal with the
computation of simple interest.
Formula 1: The Amount of Simple Interest
tI Pr
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.
Take Note:
In simple interest, the amount of interest
earned per annum is constant.
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.
Example 68:
What amount of interest will be charged on the loan of Ms. Bea
Ky of P7,300.00 borrowed for 3years at a simple interest rate of
12% per annum?
Final Answer:
The principal will earn an interest of
P2,628.00.
Example 69:Nimfa Bebe deposited P5,000.00 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.
Example 70:
Miss. Honeygirl Pulut-pukyutanborrowed P5,200.00 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?
Take Note:
What should we do when rate or percentage
of interest (r) is unknown?
Classroom Task :
Derive the formula for finding the rate
of interest.
Formula 2: The Rate of Interest
Pt
Ir
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.
Example 71:
The simple interest received over a period of 5 years and 3
months on a loan of P22,000.00 is P11,300.00. Compute the rate of interest.
Something to think about…
What should we do when duration of the loan/ time
(t) is unknown?
Classroom Task :
Derive the formula for finding
the time.
Formula 3: The Duration of the Loan/ Time
Pr
It
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.
Example 72:Lhady_ZsUpFlaDeeTa borrowed P5,000.00 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?
Example 73:
TrOuFHaNG_QOuLLheTszpaid an amount P13, 620.00
for a loan P25,600.00 at 10.5% interest rate. Find the
duration of the term?
Something to think about…
What should we do when Principal (P) is
unknown?
Classroom Task :
Derive the formula for finding the principal
amount.
Formula 4: The Principal Amount
rt
IP
Formula 4: The Principal Amount
This shall be used in computing the Principal when
amount of interest, rate of interest and time are given.
Example 74:
bHozSS_mHapA6mahAL paid
an interest of P2,800.00 on a
loan for 2 years at 9.5% interest rate. How much was
the original loan?
Performance Task 13:
Please download, print
and answer the “Let’s
Practice 13.” Kindly work
independently.
Lecture 16: The Maturity Value and the Present Value of the
Simple InterestSHMth1: General Mathematics
Accountancy, Business and
Management (ABM)
Mr. Migo M. Mendoza
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.
The Maturity Value (F)
Maturity Value denoted by Fis also called as the
“accumulated value,” “future value,” and “final
value.”
The Maturity Value (F)
In other words, maturity value is equal to the sum of the
amount of principal and the amount of interest.
Classroom Task :
Derive the formula for finding the maturity
value (F).
Formula 6: The Maturity Value (F)
)1( rtPF
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.
Example 75:
Miss Bea Bunda deposited an amount of P12,800.00 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?
Example 76:
Mr. Hagardo Versoza paid an interest of P5,000.00 on a loan for 3 years at
8% simple interest. Compute the value of:
a) the original loan; andb) the amount Mr. Versosa paid
at the end of 3 years.
Something to think about…
Based on our previous example, what is now
the present value?
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.
The Present Value (P)
Since the present value is actually the principal, we
will denote it using majuscule letter P.
Classroom Task:
Derive the formula for finding the present
value (P).
Formula 6: The Present Value (P)
)1( rt
FP
Formula 6: The Present Value (P)
This shall be used in computing the present value given the maturity value, rate
and time.
Example 77:
Determine the present value of an investment which
accumulated to P48,600.00in 6 years at 6% simple
interest.
Example 78:
The maturity value paid on a loan is P72,000.00. 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.
Something to think about…
Based on our previous example, what is the easiest
way to compute the total amount of interest (I)?
Formula 7: The Total Interest
PFI
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.
Performance Task 14:
Please download, print
and answer the “Let’s
Practice 14.” Kindly work
independently.
Lecture 17: The Exact and the Ordinary Interests
SHMth1: General Mathematics
Accountancy, Business and
Management (ABM)
Mr. Migo M. Mendoza
A Short Recap…
When the term of investment is expressed in days, what would be the approach in computing
for the amount of interest?
The Two ApproachesTwo Approaches in Computing for the Amount of
Interest Given the Time in Dates:
1. Exact Interest Method2. Ordinary Interest Method
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.
The Exact Interest
To denote Exact Interest we will use the symbol Ie
(majuscule letter I and subscript minuscule letter e).
Formula 8: The Exact Interest (Ie)
366
Pr
365
Pr torI
tI ee
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.
The Ordinary Interest (Io)
This is used when interest is computed on the
basis of an assumed 30-day/month or 360-
day/year.
The Ordinary Interest (Io)
To denote Ordinary Interest we will use the symbol Io
(majuscule letter I and subscript minuscule letter o).
Formula 9: The Ordinary Interest (Io)
360
Pr tIo
Formula 9: The Ordinary Interest (Io)
This shall be used in computing for the ordinary interest, given the principal
amount, the rate of interest and time per days.
Example 79:Mr. Benny Bilang invested an amount of P28,100.00 at 7%
simple interest for 100 days. Compute the value of the:
1) exact interest; and2) ordinary interest.
Example 80:Miss Lily Mangipin deposited an amount of P12,800.00 in a time
deposit account at 8% simple interestfor 150 days. Compute the value of the:
exact interest; and the maturity valueat the end of the term.
Performance Task 15:
Please download, print
and answer the “Let’s
Practice 15.” Kindly work
independently.
Lecture 18:
Time between Two DatesSHMth1: General Mathematics
Accountancy, Business and
Management (ABM)
Mr. Migo M. Mendoza
Something to think about…
If two dates are given,
how can we determine
the number of days?
Example 81:
Determine the number of days from
September 21, 2017 to March 14, 2018.
Loan Date:
This is the first day the loan/ deposit/ investment was made. It is also called
as the “origin date.”
Hence,
In our previous example the loan date
or origin date is September 21, 2017.
Maturity Date
This is the last day of the loan/ deposit/ investment. It
is also called as the “due date.”
Hence,
In our previous example the loan date
or origin date is March
14, 2018.
Did you know?
There are two ways in
determining the
number of days given
two dates.
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
The Actual Time (Ac)
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.
The Approximate Time (Ap)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.
Something to think about…
How can we determine
which are 30-day month
and which are not?
The Knuckle Months MethodThe 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.
The Knuckle Months Method
Example 81: Determine the number of days
from September 21, 2017 to
March 14, 2018 using actual and approximate time
methods.
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.
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.
Steps in Determining the Number of Days Given Two Dates
Step 2:
Write the number of days in each succeeding month.
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.
Steps in Determining the Number of Days Given Two Dates
Step 4:
Add the days from the first month to the last month.
Example 82:Determine the actual and
approximate time from February 1, 2016 to December 25, 2016.
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.
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 Method2.Actual Time, Exact Interest Method
3.Approximate Time, Ordinary Interest Method
4.Approximate Time,Exact Interest Method
Formula 10: Actual Time, Ordinary Interest Method
360
Pr co
AI
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.
Formula 11: Actual Time, Exact Interest Method
365
Pr ce
AI
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.
Formula 12: Approximate Time, Ordinary Interest Method
360
Pr p
o
AI
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.
Formula 13: Approximate Time, Exact Interest Method
365
Pr p
e
AI
Example 83:An amount of P18,000.00 was invested
to McDollibee at 8% simple interest on May 25, 2016. How much shall be the
amount of interest earned on October 12, 2016 using the four methods of
computing period t?
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.
Something to think about…
Why do you think most
of the lenders or banks
love to use banker’s
rule?
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!
Example 84:On December 25, 2011, LIBING Things
Funeral Parlor deposited an amount of P15,800.00 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.
Performance Task 16:
Please download, print
and answer the “Let’s
Practice 16.” Kindly work
independently.