LESSON 4LESSON 4

BASICS OF SIMPLE INTEREST

Learning OutcomesLearning Outcomes• By the end of this lesson, students

should be able to:– Calculate simple interest.– Calculate maturity value.– Calculate the exact number of days

from one date to another in a loan period.

– Find the due date of a loan.– Find the exact and ordinary interest.– Find the principal, rate and time of the

simple interest.– Define the basic terms used with

promissory notes.

List of TopicsList of Topics

• 3.1 Calculate simple interest• 3.2 Calculate maturity value• 3.3 Calculate the exact number of days

from one date to another in a loan period

• 3.4 Find the due date of a loan• 3.5 Find the exact and ordinary interest• 3.6 Find the principal, rate, and time of

the simple interest• 3.7 Define the basic terms used with

promissory notes

Simple interestSimple interest• Interest is a fee charged for borrowing

money or returns on investment or savings in financial institutions. There are two types of interest commonly used nowadays: simple interest and compound interest. Simple interest involves interest only on the principal, while compound interest requires interest to be paid on both principal and the previously earned interest. For this topic, discussion will be on simple interest only.

• Simple interest is interest charged or returns on the entire principal for the entire length of the loan.

• Interest = Principal x Rate x TimeI =PRT

Where: • I – Interest, the amount charged or earned for

any loan or deposit.• P – Principal, either the loan amount or the

amount invested.• R – Rate, the percent charged for borrowing

money or percent earned for investment.• T – Time, the loan period or investment period

written in terms of number of years.• If it is written in terms of month/week/day,

convert it to a fraction of a year.• For example, 3 months loan, will be written as

3/12

ExampleExampleCalculate the interest earned

from an investment of RM 20,000 at 6% invested for two months

Solution:I =PRT

20,000 X 0.06 X 2/12 = RM 200

Maturity valueMaturity value• The maturity value It is the total value of a loan or an

investment. The total value is the principal plus the interest. Maturity value is the amount that must be repaid when the loan is due, or total amount earned at the end of the investment period.

Maturity value = Principal + Interest

M =P +I

ExampleExampleFind the maturity value of a RM

80,000 loan borrowed for three months at 6%.

The interest chargedI =PRT

80,000 X 0.06 X 3/12 = RM1,200 The maturity value of the loan =

RM80,000 + 1, 200 = RM81,200

Computing the exact number of Computing the exact number of days from one date to another in a days from one date to another in a loan periodloan periodIt is common for loans to be given

in certain number of days, such as 90 days or 120 days from a given date or a loan may be due on a fixed date such as February 24.

In applying the I = PRT formula, we need to find the number of days from one date to another by referring to the number of each day of the year table.

ExampleExample• Find the number of days from February 10 to

August 25• Solution:• Find 10 at the leftmost column of the number of

each day of the year table.• Go across that row until it intersects with the

column headed by February. • The number of that intersection is 41, meaning

that February 10 is on the 41st day of the year. • Next find August 25, which is 237th day of the

year. • Deduct the difference in day of the year to find

the number of days in the loan period: • August 25 is day 237• February 10 is day -41• = 196

Find the due date of a Find the due date of a loanloan• There are cases where the loan is due in a

certain number of days. If the date the loan is given is known, then the date it is due can also be found by using the number of each day of the year table

• Example• Date loan was made: Jan 3, Term of loan:

100 days. When is the due date of the loan?

• Solution• (Jan 3) 3 + 100 days = 103• Refer to table for day 103. The due date is

April 13.

Exact and ordinary Exact and ordinary interestinterest• When time period is in days, instead of

year or months, there are two methods commonly used to calculate time (for Time in Interest formula).

• Exact interest - uses 365 as the number of days in a year.

• Ordinary interest or banker’s interest - uses 360 as the number of days in a year.

• Financial institutions usually use ordinary interest as it produces more interest.

solutionsolution

Exact interest formula Ordinary interest formula

365

periodloan ain days ofnumber T

360

periodloan ain days ofnumber T

Find the interest earned from RM 61,000 investment made by Aisyah for 150 days at 12%. Calculate using both the exact interest and ordinary interest.

Exact interest Ordinary interest

15061,000 0.12

3653,008.22

EI PRT

RM

RM

15061,000 0.12

3603,050

OI PRT

RM

RM

Finding of the principal, rate Finding of the principal, rate and time of the simple and time of the simple interestinterestThis section explains the use of I =

PRT in different forms. It is used to calculate principal, rate or time, given either interest or any of the other two values is known.

Finding the principal.When interest, rate, and time are

known, the principal can be computed using the following formula

Finding the principal.Finding the principal.

TimeRate

Interest

RT

IP Principal =

ExampleExampleCalculate the principal of a 6%

note that earned RM 160 in 60 days.

Finding the rateFinding the rate

PT

IR

TimePrincipal

InterestRate =

ExampleExample

09.0

360

6016,000 RM

240 RMR

The rate is 9%.

Finding the timeFinding the time

PR

IT

RatePrincipal

InterestTime =

Example Example

Find the time, stated in years; it will take a RM 6,000 loan to earn RM 400 interest at a 5% rate.

Solution:

years 3

11or years 333.1

0.056,000 RM

400 RM

PR

IT

Promissory notePromissory note• It is a written promise to pay a certain

sum of money on a specific future date by one person or firm to another person or firm. It is a legal document between lender and borrower.

• Some promissory notes are non-interest-bearing. The borrower pays back only the amount borrowed at maturity. However, most notes are interest bearing.

• The following is an example of an interest-bearing note:

Promissory notePromissory note

PROMISSORY NOTE

Puchong, Selangor,

Ninety days after date, _ I_ promise to pay to the order of

Danish Mohamad ____________ /_____________ RM750.00_______

___Seven hundred fifty ringgit__ with interest at __12% per year__

Payable at __, Kelana Jaya.__

Due _January 25, 2010_ Asma’ Abu Bakar

• The above promissory note is called interest bearing promissory note. It is a legal document that promises to pay a certain amount of money at a determined future date.

• Below are the terms of a simple interest promissory note.• Maker : Danish Mohamad

• Payer : Asma’ Abu Bakar

• Payee : Asma’ Abu Bakar

• Face value : RM 750.00• Term of loan (Length of time until the note is due) : 90

days• Date loan was made : October 27, 2005• Date loan is due : January 25, 2006• Maturity value (Principal + interest) : RM 772.50

• Calculation for interest charged and maturity value of the note are shown below

22.50 RM

360

9012.0750 RM

PRTI

772.50 RM

22.50 RM 750 RM

IPM

Lesson SummaryLesson Summary

• This topic explains the method of calculating simple interest. It is a one-time interest charged to the entire principal. It uses the formula . Students are also introduced to the interest bearing promissory notes and the calculations involved.

• Next topic would cover lessons on discounting promissory notes before its maturity. Students must have good understanding of simple interest as prerequisite for understanding the next topic.