simple interest

7/21/2019 Simple Interest

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FACULTY GUIDANCE NOTES FOR

SIMPLE INTEREST AND COMPOUND INTEREST

(Ref: FGN101003)

Examples to be taken in the class:

Introduction:

Ex 1:

The table gives an example of how simple interest (SI) and compound interest (CI) operate . The principal at the

beginning of 1styear of !s.1"""" and a rate of 1"# p.a. are considered. The details for $ years are shown.

Under SI Under CI

%rincipal at the Interest Interest till &mount at %rincipal at Interest Interest till &mount at

'ear beginning of for the the end of the end of the beginning for the the end of the end of

the year year the year the year of the year year the year the year

1 1"""" 1""" 1""" 11""" 1"""" 1""" 1""" 11"""

1"""" 1""" """ 1""" 11""" 11"" 1"" 11""

1"""" 1""" """ 1""" 11"" 11" 1" 11"* 1"""" 1""" *""" 1*""" 11" 11 *+*1 1*+*1

$ 1"""" 1""" $""" 1$""" 1*+*1 1*+*.1 +1"$.1 1+1"$.1

&ll figures are in !s. &% &% ,% ,% ,%


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Ex 15: & sum of money triples at compound interest

in - years. In how many years will it become

- times itself

Ex 16: /ind the difference between the SI and CI

(compounded annually) on !s.$"" at

1"# p.a. for years.

Ex 17: &t what rate of SI will a sum become five

times itself in " years

Ex 18: Saritha invested !s.$"""" for years

interest being compounded annually. If the

rate of interest is 0# 1"# and 1#

respectively for 1st nd and rd years then

find the interest earned by Saritha.


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/aculty member can uic2ly write the below mentioned table on top half of the board and should go on to explain

the observations that can be made from it.

The table gives an example of how simple interest (SI) and compound interest (CI) operate . The principal at the

beginning of 1styear of !s.1"""" and a rate of 1"# p.a. are considered. The details for $ years are shown.

Under SI

Under CI

%rincipal at the Interest Interest till &mount at %rincipal at Interest Interest till &mount at

'ear beginning of for the the end of the end of the beginning for the the end of the end of

the year year the year the year of the year year the year the year

1 1"""" 1""" 1""" 11""" 1"""" 1""" 1""" 11"""

1"""" 1""" """ 1""" 11""" 11"" 1"" 11""

1"""" 1""" """ 1""" 11"" 11" 1" 11"

* 1"""" 1""" *""" 1*""" 11" 11 *+*1 1*+*1

$ 1"""" 1""" $""" 1$""" 1*+*1 1*+*.1 +1"$.1 1+1"$.1

&ll figures are in !s. &% &% ,% ,% ,%

Obserations that can be made(Comparison between SI and CI)3

SI CI

1. %rincipal at the beginning of each year is same 1. %rincipal at the beginning of each year is different and

i.e. principal for any years remains same. the amount at the end of a year is the principal for the

consecutive year.

. The interest for any two years remains constant. . The interest for no two years is the same.

. /aculty should emphasi4e here that year after . The interest is added to the principal at the end of

year even though the interest gets accumulated each compounding period (1 year in this case) to

and is due to the lender this accumulated interest arrive at the new principal for the next compounding

is not ta2en into account for the purpose of period. In other words the amount at the end of each

calculating interest for later years. compounding period would be the principal for the

next compounding period.

*. Interest till the end of consecutive years and *. Interest for the successive years amount at the end of

amount at the end of consecutive years are in &.%. consecutive years are in ,.%.

/.5. may ta2e the following uestion and show the students as to how the table can be used.


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i.e. 1" -1"" 6 +""

(because SI for years 6 1"" hence SI for

1 year 6 6 +"")

" 6 +r

r 6 $#

SI 61""

+"" 61""

% 6 1"""

. The difference between the CI for 2 years and CI

for (2 7 1) years is eual to the interest for one

year on the amount at the end of 2thyear.

i.e. CI(for 2 7 1 years)-CI(for 2 years)

6 &(end of 2th year)1""

*. The above mentioned point can also be

expressed in terms of the amount.

i.e. C&(for 2 7 1 years)-C&(for 2 years)

6 &(end of 2th year)1""

Ex !:

& sum under CI interest being compounded

annually amounts to !s.+""" in two years

and !s.-"" in three years. /ind the rate of

interest.

Sol: &s we already 2now that

C&for years-C&for years6 C&for years1""

-"" -+""" 6 +"""1""

1"" 6 +"r

r 6 "#

$. The difference between the CI for the 2 thyear and

the CI for the (2 7 1)thyear is eual to the interest

for one year on CI for the 2 thyear.

CIfor (2 +1)th year - CIfor 2th year= CIfor 2th year1""

Ex 5: The compound interest on a certain sum for

the third and the fourth years is !s.101$ and

!s.188+.$ respectively. 9hat is the rate of

interest

Sol: 9e 2now that

CIfor (2 +1)th year - CIfor 2th year= CIfor 2th year1""

CIfor *th year - CIfor )rd year= CIfor )rd year1""


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Compoundin" more than once in a #ear:

Compounding can also be done more freuently than

once in a year i.e. once in every six months every *

months every months every month etc.

If the compounding is done more than once in a year

then in the earlier discussed formula forn

&n6 % 1+1""

where r 6 rate of interest per annu m should be

changed to rate of interest per compounding period.

i.e. given r# per annum

rnew6 per compounding period2

where 2 is number of compounding periods in a year.

Similarly n in the formula where n 6 number of years

should be changed to total number of compounding

period s.

i.e. nnew 6 2 n where 2 is number of compounding

periods in a year.

Ex:,iven r 6 1# p.a. and n 6 years then

(a) if compounding is done half yearly (i.e.


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% 1+

6 : 7 : 7 . . .1"" 1"" 1""

. . 7 :.

Ex 11: In 0 years a certain sum doubles itself under

simple interest. In how many years will the

sum becomes three times itself

Sol: Time ta2en to earn interest (which is 1""# of

the principal) is 0 years.

Time ta2en to earn interest (which is

""# the principal) is "" 6 1+ years.1""

Ex 1$: & sum of money triples at compound interestin - years. In how many years will it become

- times itself

Sol: ;et the sum be !s.%.

,iven that the sum triples (i.e. it becomes

%) after - years.


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SI CI

1styear $+2 "2

ndyear $+2 *"2 "+ "1+

>>>>>> >>>>>>

$12 ++"2

=ifference between interests is++"2 -$12 6 1*02

1*02 !s.-

2 6*

% 6 $1" 6 10".*

Ex 17: ,iven the difference between SI for years

and CI for years on the same sum and at

the same rate of interest compounded

annually is !s.1". The difference between

SI for years and CI for years on the same

sum and at the same rate of interest is

!s.++. /ind the rate of interest.

Sol:

-%- 6 ++

1"" 1""

r

1""

r ++

1"" 1"

simple interest

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