2. Find the difference between simple interest and compound interest

1.	2. Find the difference between simple interest and compound interest on Rs. 15,000 at 8 p.c.p.a. for 3 years.
Answer» ong>Given : The PRINCIPAL is Rs. 15,000, RATE of Interest is 8 % & Time is 3 yrs . Need To Find : DIFFERENCE Between COMPOUND Interest & Simple Interest. ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ ⠀⠀⠀⠀Finding Simple Interest for finding the Difference : $\dag\:\:\it{ As,\:We\:know\:that\::}\\$ $\qquad \dag\:\:\bigg\lgroup \sf{ Simple \:Interest \:: \dfrac{P\times R \times T }{100} }\bigg\rgroup \\\\$ ⠀⠀⠀⠀Here P is the Principal , R is the Rate of Interest & T is the Time . ⠀⠀⠀⠀⠀⠀ $\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\$ $\qquad \longmapsto \sf Simple \:Interest \:= \dfrac{ 15,000 \times 8 \times 3 }{100}$ $\qquad \longmapsto \sf Simple \:Interest \:= \dfrac{ 15,0\cancel {00} \times 8 \times 3 }{\cancel {100}}$ $\qquad \longmapsto \sf Simple \:Interest \:= 150 \times 8 \times 3$ $\qquad \longmapsto \sf Simple \:Interest \:= 150 \times 24$ $\qquad \longmapsto \frak{\underline{\purple{\:Compound\:Interest\:= Rs.36,00 }} }\bigstar \\$ Therefore, ⠀⠀⠀⠀⠀ $\therefore {\underline{ \mathrm {\:Simple \:Interest \: \:is\:\bf{Rs.3,600}}}}\\$ ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ Now , We have to find Compound Interest so for Compound Interest we have to first find the Amount, ⠀⠀⠀⠀Finding Amount : $\dag\:\:\it{ As,\:We\:know\:that\::}\\$ $\qquad \dag\:\:\bigg\lgroup \sf{ Amount \:: P \bigg( 1 + \dfrac{R }{100}\bigg) ^T }\bigg\rgroup \\\\$ ⠀⠀⠀⠀Here P is the Principal , R is the Rate of Interest & T is the Time . ⠀⠀⠀⠀⠀⠀ $\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\$ $\qquad \longmapsto \sf Amount = 15,000 \bigg( 1 + \dfrac{8}{100}\bigg)^3 \\$ $\qquad \longmapsto \sf Amount = 15,000 \bigg( 1 + \cancel {\dfrac{8}{100}}\bigg)^3 \\$ $\qquad \longmapsto \sf Amount = 15,000 \bigg( 1 + 0.08\bigg)^3 \\$ $\qquad \longmapsto \sf Amount = 15,000 \bigg( 1.08\bigg)^3 \\$ $\qquad \longmapsto \sf Amount = 15,000 \times 1.259712 \\$ $\qquad \longmapsto \frak{\underline{\purple{\:Amount = Rs.18,895.68 }} }\bigstar \\$ Therefore, ⠀⠀⠀⠀⠀ $\therefore {\underline{ \mathrm {\:Amount \: \:is\:\bf{Rs.18,895.68}}}}\\$ ⠀⠀⠀⠀Now , Finding Compound- Interest : $\dag\:\:\it{ As,\:We\:know\:that\::}\\$ $\qquad \dag\:\:\bigg\lgroup \sf{ Compound \:Interest \:: Amount- Principal }\bigg\rgroup \\\\$ ⠀⠀⠀⠀Here Amount is Rs.18,895.68 & Principal is Rs.15,000 . ⠀⠀⠀⠀⠀⠀ $\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\$ $\qquad \longmapsto \sf Compound \:Interest \:= 18,895.68 - 15,000$ $\qquad \longmapsto \frak{\underline{\purple{\:Compound\:Interest\:= Rs.3,895.68 }} }\bigstar \\$ Therefore, ⠀⠀⠀⠀⠀ $\therefore {\underline{ \mathrm {\:Compound \:Interest \: \:is\:\bf{Rs.3,895.68}}}}\\$ ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ ⠀⠀⠀⠀⠀Now Finding Difference between Compound interest and Simple Interest : $\dag\:\:\it{ As,\:We\:know\:that\::}\\$ $\qquad \dag\:\:\bigg\lgroup \sf{ Difference \:: Compound \:Interest\:-\:Simple\:Interest.}\bigg\rgroup \\\\$ ⠀⠀⠀⠀⠀Here Compound interest is Rs.3,895.68 & Simple Interest is Rs.3,600 . ⠀⠀⠀⠀⠀⠀ $\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\$ $\qquad \longmapsto \sf Difference \:= 3,895.68 - 3,600$ $\qquad \longmapsto \frak{\underline{\purple{\:Difference \:= Rs.295.68 }} }\bigstar \\$ Therefore, ⠀⠀⠀⠀⠀ $\therefore {\underline{ \mathrm {\:Difference \:Between \:Compound \:Interest \:and\:Simple \:Interest \:is\:\bf{Rs.295.68}}}}\\$ ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

2. Find the difference between simple interest and compound interest on Rs. 15,000 at 8 p.c.p.a. for 3 years.

Answer»

ong>Given : The PRINCIPAL is Rs. 15,000, RATE of Interest is 8 % & Time is 3 yrs .

Need To Find : DIFFERENCE Between COMPOUND Interest & Simple Interest.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

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

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

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

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

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

$\qquad \longmapsto \sf Simple \:Interest \:= \dfrac{ 15,000 \times 8 \times 3 }{100}$

$\qquad \longmapsto \sf Simple \:Interest \:= \dfrac{ 15,0\cancel {00} \times 8 \times 3 }{\cancel {100}}$

$\qquad \longmapsto \sf Simple \:Interest \:= 150 \times 8 \times 3$

$\qquad \longmapsto \sf Simple \:Interest \:= 150 \times 24$

$\qquad \longmapsto \frak{\underline{\purple{\:Compound\:Interest\:= Rs.36,00 }} }\bigstar \\$

Therefore,

⠀⠀⠀⠀⠀ $\therefore {\underline{ \mathrm {\:Simple \:Interest \: \:is\:\bf{Rs.3,600}}}}\\$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

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

⠀⠀⠀⠀Finding Amount :

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

$\qquad \dag\:\:\bigg\lgroup \sf{ Amount \:: P \bigg( 1 + \dfrac{R }{100}\bigg) ^T }\bigg\rgroup \\\\$

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

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

$\qquad \longmapsto \sf Amount = 15,000 \bigg( 1 + \dfrac{8}{100}\bigg)^3 \\$

$\qquad \longmapsto \sf Amount = 15,000 \bigg( 1 + \cancel {\dfrac{8}{100}}\bigg)^3 \\$

$\qquad \longmapsto \sf Amount = 15,000 \bigg( 1 + 0.08\bigg)^3 \\$

$\qquad \longmapsto \sf Amount = 15,000 \bigg( 1.08\bigg)^3 \\$

$\qquad \longmapsto \sf Amount = 15,000 \times 1.259712 \\$

$\qquad \longmapsto \frak{\underline{\purple{\:Amount = Rs.18,895.68 }} }\bigstar \\$

Therefore,

⠀⠀⠀⠀⠀ $\therefore {\underline{ \mathrm {\:Amount \: \:is\:\bf{Rs.18,895.68}}}}\\$

⠀⠀⠀⠀Now , Finding Compound- Interest :

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

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

⠀⠀⠀⠀Here Amount is Rs.18,895.68 & Principal is Rs.15,000 .

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

$\qquad \longmapsto \sf Compound \:Interest \:= 18,895.68 - 15,000$

$\qquad \longmapsto \frak{\underline{\purple{\:Compound\:Interest\:= Rs.3,895.68 }} }\bigstar \\$

Therefore,

⠀⠀⠀⠀⠀ $\therefore {\underline{ \mathrm {\:Compound \:Interest \: \:is\:\bf{Rs.3,895.68}}}}\\$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀Now Finding Difference between Compound interest and Simple Interest :

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

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

⠀⠀⠀⠀⠀Here Compound interest is Rs.3,895.68 & Simple Interest is Rs.3,600 .

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

$\qquad \longmapsto \sf Difference \:= 3,895.68 - 3,600$

$\qquad \longmapsto \frak{\underline{\purple{\:Difference \:= Rs.295.68 }} }\bigstar \\$

Therefore,

⠀⠀⠀⠀⠀ $\therefore {\underline{ \mathrm {\:Difference \:Between \:Compound \:Interest \:and\:Simple \:Interest \:is\:\bf{Rs.295.68}}}}\\$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

2. Find the difference between simple interest and compound interest on Rs. 15,000 at 8 p.c.p.a. for 3 years.

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2. Find the difference between simple interest and compound interest on Rs. 15,000 at 8 p.c.p.a. for 3 years.​

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2. Find the difference between simple interest and compound interest on Rs. 15,000 at 8 p.c.p.a. for 3 years.