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## INTEREST n compound week 2 - edited - Copy

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# Simple & Compound Interest

### INTEREST n compound week 2 - edited - Copy

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

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

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….