Question

2. Calculate the amount and the compound interest on Rs. 64000 for 3 years at 7% per annum compounded annually.​

Answer 1

Given : Principal ( P ) is Rs.64,000 , Rate of Interest ( R ) is 7 % p.a. & Time ( T ) is 3 years .

Exigency To Find : Amount and Compound interest.

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⠀⠀⠀⠀⠀Finding Amount :

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

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

⠀⠀⠀⠀⠀⠀Here , P is the Principal , T is the Time & R is the Rate of Interest at the rate of per annum.

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

$\qquad :\implies \sf Amount \:= \: P \bigg( 1 + \dfrac{R}{100} \bigg)^T$

$\qquad :\implies \sf Amount \:= \: 64,000 \bigg( 1 + \dfrac{7}{100} \bigg)^3$

$\qquad :\implies \sf Amount \:= \: 64,000 \bigg( 1 + 0.07 \bigg)^3$

$\qquad :\implies \sf Amount \:= \: 64,000 \bigg( 1.07 \bigg)^3$

$\qquad :\implies \sf Amount \:= \: 64,000 \times 1.225043$

$\qquad :\implies \bf Amount \:= \: 78,402.752$

$\qquad:\implies \frak{\underline{\purple{\:Amount \:= \: Rs.\:78,402.752 }} }\:\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Amount\: \:is\:\bf{Rs.\:78,402.752}}}}$

⠀⠀⠀⠀⠀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. 78,402.752 & Principal is Rs. 64,000 .

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

$\qquad:\implies \sf Compound\:Interest\:\:= \; Amount\:- \: Principal\:$

$\qquad :\implies \sf Compound \:Interest \: \:= \: 78,402.752 \: - \: 64,000$

$\qquad :\implies \bf Compound \:Interest \:= \: 14,402.752 \:$

$\qquad:\implies \frak{\underline{\purple{\:Compound \:Interest \:= \: Rs.\:14,402.752 }} }\:\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Compound \:Interest \: \:is\:\bf{Rs.\:14,402.752}}}}$

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