Question

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

Answer 1

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,

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

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Answer 2

Solution!!

Principal (P) = Rs 15000

Rate of interest (R) = 8%

Time (T) = 3 years

Interest = (P × R × T)/100

Interest = (15000 × 8 × 3)/100

Interest = 150 × 8 × 3

Interest = Rs 3600

Simple interest = Rs 3600

_______________________________

Principal (P) = Rs 15000

Rate of interest (R) = 8%

Time (n) = 3 years

Amount = P(1 + (R/100))³

Here 3 is the time (n).

Amount = 15000(1 + (8/100))³

Amount = 15000(108/100)³

Amount = 15000 × (108/100) × (108/100) × (108/100)

Amount = Rs 18895.68

CI = Amount - Principal

CI = Rs 18895.68 - Rs 15000

CI = Rs 3895.68

Compound interest = Rs 3895.68

Simple interest = Rs 3600

Difference between them = Rs 3895.68 - Rs 3600

Difference between CI and SI = Rs 295.68