CHAPTER 1

CHAPTER 1

SIMPLE INTEREST

LEARNING OBJECTIVES

By the end of this chapter, you should be able to
1. Explain the concept of simple interest
2. Use the simple interest formula to calculate interest, interest rate, time and dates
with data provided
3. Use the simple amount formula to calculate the present and future values of
some investments
4. Identify four concepts of exact simple interest, ordinary simple interest, exact
time and approximate time
5. Apply Banker’s Rule to some investments and loan problems
6. Use the concepts of equation of values to solve investment and loan problems

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1.1 INTRODUCTION

INTEREST

LOAN

Briefly explain the definition of interest in your own words

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1.2 SIMPLE INTEREST FORMULA

In simple interest, the interest will be based on the original principal for the
entire period of the investment or loan. This is mean that the principal will not change
from time to time. It is the product of the principal multiplied by the rate and time.
This may be stated as the formula

Simple interest Rate

I = Prt

Time (in year)

Principal / Face value

Yearly calculation
Suppose that a person borrows RM1,000 at a rate of 8% per annum for a period

of 4 years. Find the amount of interest that he needs to pay.

Solution:

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Using the same question (above), calculate by using formula of simple interest.
Solution:

Example 1
Hafiz borrows RM7,000 for 3 years at 5.5% per annum simple interest. How much is the
interest charged?
Solution:

Example 2
RM1,000 is invested for two years in a bank, earning a simple interest rate of 8% per
annum. Find the simple interest earned.
Solution:

Simple interest calculation is always based on the original principal, no matter how long
the principal is invested.

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Example 3
Mr. Aru deposited RM6000 in a bank and obtained RM120 simple interest after three
months. Find the simple interest rate offered.
Solution:

1.3 SIMPLE AMOUNT FORMULA
The simple amount, S is the sum of the original principal and the interest earned.

Principal + P+I P + Prt P(1+rt)
Interest

S = P(1+rt)

Simple amount also known as maturity value or future value.

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Example 4
RM10,000 is invested for 4 years 9 months in a bank earning a simple interest rate of
10% per annum. Find the simple amount at the end of the investment period.
Solution:

Example 5
Raihan invests RM5,000 in an investment fund for three years. At the end of the
investment period, his investment will be worth RM6,125. Find the simple interest rate
that is offered.
Solution:

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Example 6
Siti obtained a RM2,000 loan from a bank which charges an interest of 7.5%. Siti intends
to settle the loan after 2 years.

a) Calculate the amount of interest Siti will need to pay.
b) What is the maturity value of Siti’s loan.
Solution:

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QUICK CHECK 1A

1. Mr. Shuib deposited RM6,000 in a bank and obtained RM120 simple interest
after three months. Find the simple interest rate offered.

2. Sazali invests RM3,600 at 4.5% simple interest in a bank. Find the amount in the
account after nine months.

3. Ms. Deepa deposited RM4,000 in a bank and obtained simple interest of RM300
after three years. What was the simple interest rate offered? How much interest
could she earn if she deposited RM15,000 in the bank for eight months?

4. Rahimi invests RMX in a bank. After 48 months, his investment will be worth
RM6,500. If the simple interest rate is 6.5% per annum, find the value of X.

5. Laili opened an account for her son when he was one. Her initial deposit was
RM500. Suhaila depaosited another RM800 into the account on her son’s second
birthday. The account earns an interest of 6% per annum. Find the amount in
the account after 5 years.

6. Two years ago, Kimi invested RM P in his account which earns r% simple interest.
After 18 months, he noticed that the amount had become RM10,450 and today
the amount is RM10,600. Find the value of P and r.

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1.4 FOUR BASIC CONCEPTS
The length of time for a deposit or a loan is not always given in years. If the

period is short, it may also be expressed in months or days.
They are two ways to calculate the number of days from one date to another

and the number of days per year for interest computation.

Calculating the number of days Calculating the interest
Exact time Exact simple interest

It is the exact number of days between This uses a 365/366-day year for interest
two given dates computation

Approximate time Ordinary simple interest

It assumes a month has 30 days in the This uses a 360-day year for interest
calculation of number of days between computation

two given dates

Example 7

RM1,000 was invested on 15 March 2015. If the simple interest rate offered was 10%
per annum, find the interest received on 29 August 2015 using

a) Exact time and exact simple interest
b) Exact time and ordinary simple interest
c) Approximate time and exact simple interest
d) Approximate time and ordinary simple interest

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Solution:

Method (b) is called Banker’s Rule. This method
is used by banks in USA and in international
business transactions but not in Malaysia.

BUT

We shall use the exact time and 360-day year
in the interest discussions

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Example 8
Samy borrowed RM5,000 from a bank on 30 March 2012. If the accumulated amount is
RM5,021.67 and the simple interest rate is 6% per annum, find the date of repayment
using Banker’s Rule.
Solution:

Example 9
On 10 March 2011 Emmy deposited RMX in an account that paid 8% per annum simple
interest. On 28 August 2011, she withdrew RM8,000 from the account and the balance
in the account was RM4,000. Find the initial deposit RMX using the Banker’s Rule.
Solution:

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1.5 PRESENT VALUE

Present value is today’s value of a sum of money. For example, suppose a person
wants to have a certain amount of money after a certain term. He needs to invest some
amount of money today in order to receive a sum of money on the future. The money
he invests today is called the present value. It is also known as the principal, P while
the amount of money that is going to be received in the future is maturity value, S.

TODAY/PRESENT FUTURE / MATURITY

P S = P(1+rt)
SP = S(1 + rt)-1

Example 10
How much ought to be invested today to yield RM10,000 after 5 years. Assume that the
account in which the money is to be invested is one which earns an interest of 10%.
Solution:

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Example 11
A man obtained a personal loan on April 10, 2015. He repaid RM3,952 on October 7,
2015 thereby settling the loan in full. If the interest charged was 8%, how much did he
borrow?
Solution:

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QUICK CHECK 1B
1. A person obtains a RM3,500 loan from a bank that charges an interest of 7.25%.
The loan was obtained on May 10, 2016 and matures on September 14, 2016.
What is the maturity value of the loan?

2. Muthusamy’s application for a personal loan of RM21,000 was approved on July
5, 2015. On that day, Muthusamy opened a savings account and the loan was
deposited into that account. On August 8, 2015, Muthusamy added RM2000 to
the savings account. On October 12, 2015, he updated his savings book. How
much should be in his account if the account pays an interest of 5% per annum?

3. A sum of money was deposited on 3 March 2014 in an investment fund which
offered 7% simple interest. On 12 June 2014, RM2,800 was withdrawn from the
fund. Find the initial deposit using Banker’s Rule.

4. A loan was given out on 28 August 2018 at 7% simple interest. It was paid up
on 31 December 2018 with a payment of RM9,299.25. Find the loan amount
using the Banker’s Rule.

5. Rozana made two deposits into an investment account. She made first deposit
on February 2, 2015 and the second deposit of RM400 on May 13, 2015. When
she checked the account on August 1, 2015, it was worth RM2,500. The interest
earned was 9% simple interest. What was the value of the initial deposits?

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1.6 EQUATION OF VALUE

An equation that states the equivalence of two sets of dated values at a stated
date is called an equation of value or equivalence. The sated date is called the
focal date, the comparison date or the valuation date.

The following procedure should be carried out in order to set up and solve the
equation of value.

1. Draw a time diagram with all the dated values
2. Select the focal date
3. Pull all the dated values to the focal date using the stated interest rate
4. Set up the equation of value and then solve

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Example 12
A debt of RM800 due in four months and another of RM1,000 due in nine months are
to be settled by a single payment at the end of six months. Find the size of this payment
using
a) The present as the focal date
b) The date of settlement as the focal date
assuming money is worth 6% per annum simple interest.
Solution:

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Example 13
A debt of RM500 due two months ago and RM900 due in nine months are to be settled
by two equal payments, one at the end of three months and another at the end of six
months.
Find the size of the payments using
a) The present as the focal date
b) The end of six months as the focal date
assuming money is worth 10% per annum simple interest.
Solution:

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QUICK CHECK 1C

1. A debt of RM800 due in four months and another of RM1,000 due in nine months
are to be settled by a single payment at the end of six months. Find the size of
this payment using
a) The present as the focal date
b) The date of settlement as the focal date

assuming money is worth 6% per annum simple interest.

2. A debt of RM500 due two months ago and RM900 due in nine months are to be
settled by two equal payments, one at the end of three months and another at the
end of six months.
Find the size of the payments using
a) The present as the focal date
b) The end of six months as the focal date

assuming money is worth 10% per annum simple interest.

3. A debt of RM1,000 due in six months and another RM1,500 due in 9 months are
to be settled by a single payment at the end of 8 months. Find the size of this
payment using
a) The date of settlement as the focal date
b) The end of 6 months as the focal date

assuming money is worth 10% per annum simple interest.

4. A debt of RM500 due in 10 months and RM300 due in 3 months are to be settled
by two equal payments, one at the end of two months and another at the end of
5 months.
Find the size of payments using
a) The present as the focal date
b) The end of 10 months as the focal date

assuming money is worth 6% per annum simple interest.

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5. A debt of RM3,000 due in 6 months ago and another RM5,000 due in 18 months
are to be settled by two equal payments, one at the end of four months and the
other at the end of ten months. Find the size of the payments using
a) The presents as the focal date
b) The end of 18 months as the focal date

assuming money is worth 9% per annum simple interest.

6. Yusof borrows RM8,889 at 15% per annum simple interest. He agrees to settle the
loan by paying RM X, RM 2X and RM 3X in two months, five months and nine
months respectively. Find the value of X using the present as the focal date.