INTEREST

INTEREST

• Interest is originated from the Latin word

intereo, which means to be lost.

• Interest is then developed from the concept of

lending money that resulted in the loss to the

lender.

INTEREST

INTEREST

Interest is money Interest is charge

earned from incurred when a

investment loan or credit is

obtained/interest

is the cost of

borrowing money

PRINCIPLE = the original amount of loan/investment

INTEREST = usually expressed as percentage per annum

TWO TYPES OF

INTEREST

SIMPLE INTEREST COMPOUND

INTEREST

SIMPLE INTEREST FORMULA

• Simple interest is the interest calculated on the

original principal for the entire period it is borrowed

or invested.

Simple Interest = P * R * T

Where :

I = PRT

I = simple interest

P = principal (original amount borrowed or loaned)

R = rate of interest per annum

T = time or term in year

EXAMPLE 1

RM 1000 is invested for two years in a bank, earning a

simple interest rate of 8% per annum. Find the simple

interest earned.

Principal = RM 1000

Interest for 1st year : RM1000 x 0.08 x 1 = RM 80

Simple amount : RM 1000 + RM 80 = RM 1080

Interest for 2nd year : RM1000 x 0.08 x 1 = RM 80

Simple amount : RM 1000 + RM80 +RM80 = RM 1160

Simple interest earned : RM 80 + RM 80 = RM 160

OR

I = PRT

= 1000 x 0.08 x 2

= RM160

SIMPLE INTEREST FORMULA

I =PRT

I = RM1000 x 0.08 x 2

I = RM160

Note : The rate of interest per annum is

expressed as decimal point ( rate of

interest/100)

EXERCISE

• CALCULATE THE SIMPLE INTEREST EARNED

AND THE FUTURE VALUE IF RM 1000 IS

INVESTED FOR THREE YEARS AT 8% PER

ANNUM.

SIMPLE INTEREST

At the end of Interest earned Future Value

1st year RM1000 x 0.08 x 1 RM1000 + RM80

2nd year = RM80 = RM1080

3rd year RM1000 + RM160

RM1000 x 0.08 x 2 = RM1160

= RM160 RM1000 + RM240

= RM1240

RM1000 x 0.08 x 3

= RM240

Therefore, the simple interest earned in the 3 years is

RM240 and the future value is RM1240

SIMPLE AMOUNT FORMULA

• Simple amount formula is the sum of the

original principal and interest earned.

• Simple Amount Formula

(S) = Original Principal + Interest Earned

BY FORMULA

S = ORIGINAL PRINCIPAL + INTEREST EARNED

S=P+I

S = P + PRT

S = P ( 1+RT)

Where,

S = Simple Amount

THE SUM OF THE PRINCIPAL IS

ALSO CALLED THE FUTURE VALUE

/ MATURITY VALUE

FOUR BASIC CONCEPTS

EXACT TIME It is the exact time number of

days between two given date

APPROXIMATE TIME It is assume a month has 30 days

in the calculation of number of

days between two given date

ORDINARY SIMPLE In calculating ordinary simple

INTEREST interest, we use 360 days in year.

EXACT SIMPLE 365 or 366 days in a year for

INTEREST interest computation.

EXAMPLE 2

• FIND

A) EXACT TIME

B) APPROXIMATE TIME

FROM 15 MARCH TO 29 AUGUST OF THE

SAME YEAR

ANSWER EXACT TIME APPROXIMATE

TIME

MONTH 16 15

30 30

March 31 30

April 30 30

May 31 30

June 29 29

July 167 164

August

TOTAL

EXAMPLE 3

RM 1000 was invested on 15th March 2011. If the

simple interest rate offered was 10% per annum,

find the interest received on 29th August using :-

i. Exact time and exact simple interest

ii. Exact time and ordinary simple interest

iii. Approximate time and exact simple interest

iv. Approximate time and ordinary simple interest

CONCEPT USED ANSWER

INTEREST CALCULATION

Exact time and exact I = 1000 x 0.1 x 167/365

simple interest = RM 45.75

Exact time and ordinary I = 1000 x 0.1 x 167/360

simple interest = RM 46.39

Approximate time and I = 1000 x 0.1 x 164/365

exact simple interest = RM 44.93

Approximate time and I = 1000 x 0.1 x 164/360

ordinary simple interest = RM 45.56

COMPOUND INTEREST

• Compound interest computation is based

on the principal, which change from time

to time.

• Compound interest calculated each

period on the original principal and all

interest accumulated during past

periods.

• The principal increases from time to

time.

FORMULA

S = P ( 1 + I )n

The compound interest I is the difference between

the future value and the original principal

I=S–P

INTEREST

COMPOUND INTEREST FORMULA

A = the future value of the investment/loan, including

interest

P = the principal investment amount (the initial deposit or

loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per

year

t = the number of years the money is invested or

borrowed for

SOME IMPORTANT TERMS

Some common terms used in the relation to

compound interest are:

Original principal

Annual nominal rate

Interest period

Frequency of conversion

Period interest rate

Number of interest periods in the

investment period

EXERCISE

RM 1000 is invested for 3years. Find

the interest received at the end of

the 3 years if investment earned 8%

compounded annually.

Cont..

Example :

RM 9000 is invested for 7 years at 12% compounded

quarterly.

Original principal

Denoted by P is the original amount invested. Here, the

original principal is RM 9000.

Annual nominal rate

Denoted by K is the interest rate for a year together

with the frequency in which interest is calculated in a

year. P = 12% compounded quarterly, that is, interest is

calculated four times a year.

Cont..

Interest period

The length of time in which interest is calculated. Thus,

the interest period is 3 months.

Frequency of conversions

Denoted by “n” is the number of interest periods in a

year. In this case, n = 4

Periodic interest rate

Denoted by I interest rate for each interest period. In

this case, = r/n = 12%/4 = 3%

Number of interest periods in the investment period

Denoted by ‘n’ = nt. Thus, n = 4 x 7 = 28

SIMPLE VS COMPOUND INTEREST

SIMPLE INTEREST COMPOUND INTEREST

Simple interest is

interest paid on the Interest earned not

original principal only only the original

principal, but also on

The simple amount the all interests earned

function is linear previously

function with respect

to time Compound amount

function is an

exponential function

EXERCISE

Find the future value of RM 1000 which was

invested for..

a) 4 years at 4% compounded annually

b) 5 years 6 months at 14% compounded semi-

annually

c) 2 years 3 months at 4% compounded

quarterly

d) 2 years 8 months at 9% compounded every 2

months

EXERCISE

Find the future value for the following investment:

a) RM 20,000 at 5% compounded annually for 5 years.

b) RM 30,000 at 6% compounded semi-annually for 5

years 6 months.

c) RM 11,500 at 8% compounded quarterly for 2 ¾ years.

d) RM 120,000 at 5% compounded monthly for 3 ¼

years.

e) RM 40,000 at 12% compounded every 4 months for 6

years

f) RM 19,999 at 4.5% compounded every 2 months for 2

years

Thank You….