Question

Find the amount to be paid by Sanika at the end of 3 years , if the principal amount is Rs. 12,000 at 10% p.a. ​

Answer 1

Given : The time is 3yrs , Rate of Interest is 10 % p.a & the Principal is ₹ 12,000 .

Need To Find : The Amount in both cases [ If there is Simple Interest or if there is compund interest. ]

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⠀⠀⠀⠀Finding Amount if there is Simple - Interest :

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

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

⠀⠀⠀⠀Here P is the Principal , R is the Rate and T is the time .

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

$\qquad \longmapsto \sf Amount = 12,000 + \bigg( \dfrac{12,000 \times 10 \times 3 }{100} \bigg)$

$\qquad \longmapsto \sf Amount = 12,000 + \bigg( \dfrac{12,0\cancel{00} \times 10 \times 3 }{\cancel {100}} \bigg)$

$\qquad \longmapsto \sf Amount = 12,000 + \bigg( 120 \times 10 \times 3 \bigg)$

$\qquad \longmapsto \sf Amount = 12,000 + \bigg( 120 \times 30 \bigg)$

$\qquad \longmapsto \sf Amount = 12,000 + 3,600$

$\qquad \longmapsto \frak{\underline{\purple{\:Amount = Rs.15,600 }} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Amount\:to\:be\:paid \:when\:there\:is\:Simple \:Interest \:is\:\bf{Rs.\:\:15,600}}}}$

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⠀⠀⠀⠀Finding Amount if there is Compound - Interest :

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

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

⠀⠀⠀⠀Here P is the Principal , R is the Rate and T is the time .

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

$\qquad \longmapsto \sf Amount = 12,000 \bigg( 1 + \dfrac{ 10 }{100} \bigg)^3$

$\qquad \longmapsto \sf Amount = 12,000 \bigg( 1 + 0.1 \bigg)^3$

$\qquad \longmapsto \sf Amount = 12,000 \bigg( 1.1 \bigg)^3$

$\qquad \longmapsto \sf Amount = 12,000 \times 1.331$

$\qquad \longmapsto \frak{\underline{\purple{\:Amount = Rs.15,972 }} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Amount\:to\:be\:paid\:when\:there\:is\:Compound \:Interest \:is\:\bf{Rs.\:\:15,972}}}}$

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Answer 2

Before, finding the answer. Let's find out on how we can find the answer.

• To find the Amount, we can find the Simple Interest or Compound Interest.
• Here, we are solving by Simple Interest method.
• So, to find the Simple Interest we must use the formula of :

$\boxed{\sf Simple \: Interest = \frac{p \times r \times t}{100} }$

• Now to find the Amount, we must add the Principal and Simple Interest.

____________________

Given :

• Principal = Rs. 12,000
• Rate = 10%
• Time =  3 years

To find :

• Amount

Solution :

Simple Interest = ${\sf \dfrac{p \times r \times t}{100} }$

                          = ${\sf \dfrac{12000 \times 10 \times 3}{100} }$

                          = ${\sf \dfrac{120000 \times 3}{100} }$

                          = $\sf \dfrac{360000}{100}$

                          = 3600

∴ Simple Interest is Rs. 3600.

Amount = Principal + Simple Interest

             = 12,000 + 3600

             = 15600

∴ Amount is Rs. 15600.