Question

What will be the difference between simple interest and compound interest on sum of Rs.
6000 in 2 years at the rate of interest of 5% p.a.?
options

Rs. 15
Rs. 20
Rs. 30
Rs. 10​

Answer 1

Answer:

s.i

s.i=6000×2×5/100

=600rs

amt=6000+600

=rs.6600

c.i

for 1st year

c.i=6000×1×5/100

=300rs

amt=6000+300

=6300rs

for 2nd year

p=rs.6300

c.i=6300×1×5/100

=315rs

amt=6300+315

=rs.6615

difference between c.i and s.i =6615-6600

=rs15 (Ans)

Answer 2

Given : The Principal is Rs. 6000 , Rate of Interest is 5 % p.a. & Time is 2 yrs .

Exigency To Find : Difference Between Compound Interest & Simple Interest.

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⠀⠀⠀⠀Finding Simple Interest for finding the Difference :

$\dag\:\:\sf{ As,\:We\:know\:that\::}\\\\ \qquad \maltese \:\bf Formula \: for \: Simple \:Interest \: \::$

$\qquad \dag\:\:\bigg\lgroup \sf{ Simple \:Interest \:: \dfrac{P\times R \times T }{100} }\bigg\rgroup$

⠀⠀⠀⠀Here P is the Principal , R is the Rate of Interest & T is the Time .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad:\implies \sf Simple \: Interest \:= \: \dfrac { 6000 \times 5 \times 2 }{100}$

$\qquad:\implies \sf Simple \: Interest \:= \: \dfrac { \cancel {6000}\times 5 \times 2 }{\cancel {100}}$

$\qquad:\implies \sf Simple \: Interest \:= \: 60 \times 5 \times 2$

$\qquad:\implies \sf Simple \: Interest \:= \: 300 \times 2$

$\qquad:\implies \sf Simple \: Interest \:= \: 600$

$\qquad:\implies \frak{\underline{\purple{\:Simple \: Interest \:= \: Rs. \:600 }} }\: \;\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Simple\:Interest \:is\:\bf{Rs. \: 600 \:.}}}}$

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Now , We have to find Compound Interest so for Compound Interest we have to first find the Amount,

⠀⠀⠀⠀Finding Amount :

$\dag\:\:\sf{ As,\:We\:know\:that\::}\\\\ \qquad \maltese \:\bf Formula \:for \: Amount \: \::$

$\qquad \dag\:\:\bigg\lgroup \sf{ Simple \:Interest \:: \dfrac{P\times R \times T }{100} }\bigg\rgroup$

⠀⠀⠀⠀Here P is the Principal , R is the Rate of Interest & T is the Time .

$\qquad :\implies \sf Amount = 6,000 \bigg( 1 + \dfrac{5}{100}\bigg)^2$

$\qquad :\implies \sf Amount = 6,000 \bigg( 1 + \cancel {\dfrac{5}{100}}\bigg)^2$

$\qquad :\implies \sf Amount = 6,000 \bigg( 1 + 0.05 \bigg)^2$

$\qquad :\implies \sf Amount = 6,000 \bigg( 1.1025 \bigg)$

$\qquad :\implies \sf Amount = 6,000 \times 1.1025$

$\qquad :\implies \sf Amount = 6,615$

$\qquad :\implies \frak{\underline{\purple{\:Amount = Rs. \:6,615 }} }\:\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Amount \:is\:\bf{Rs. \: 6,615 \:.}}}}$

⠀⠀⠀⠀Finding Compound interest  :

$\dag\:\:\sf{ As,\:We\:know\:that\::}\\\\ \qquad \maltese \:\bf Formula \:for \: Compound \:Interest \:\: \::$

$\qquad \dag\:\:\bigg\lgroup \sf{ Compound \:Interest \:: Amount - Principal }\bigg\rgroup$

⠀⠀⠀⠀Here , Amount is Rs.6,615 & Principal is Rs. 6000 .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad:\implies \sf Compound \: Interest \:= \: 6,615 - 6,000$

$\qquad:\implies \bf Compound \: Interest \:= \: 615$

$\qquad:\implies \frak{\underline{\purple{\:Compound \: Interest \:= \: Rs. \:615 }} }\: \;\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Compound \:Interest \:is\:\bf{Rs. \: 615 \:.}}}}$

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⠀⠀⠀⠀Finding Difference between Compound Interest & Simple Interest  :

$\dag\:\:\sf{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Difference : \: Compound\: Interest \: - \: Simple\: Interest\:}\bigg\rgroup$

⠀⠀⠀⠀Here , Compound Interest is Rs. 615 & Simple Interest is Rs. 600 .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad:\implies \sf Difference \:= \: 615 - 600$

$\qquad:\implies \bf Difference \:= \: 15$

$\qquad :\implies \frak{\underline{\purple{\:Difference = Rs. \:15 }} }\:\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Difference \:between \:Compound \;Interest \:and \: Simple \:Interest \:is\:\bf{Rs. \: 15 \:.}}}}$

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