Question

Find the compound interest on rs. 20,000 in 2 years at the rate of 15 p.c.p.a​

Answer 1

Given :-

Principal = 20,000

Time = 2 years

Rate = 15%

To Find :-

Compound interest

Solution :-

Amount = P(1 + r/100)ⁿ

A = 20000 × (1 + 15/100)²

A = 20000 × (100 + 15/100)²

A = 20000 × (115/100)²

A = 20000 × (23/20)²

A = 20000 × 23/20 × 23/20

A = 200 × 23/2 × 23/2

A = 26450

Now

CI = Amount - Principal

CI = 26450 - 20000

CI = 6450

Answer 2

$\underline{\underline{\sf{\maltese\:Given\::-}}}$

• Principle = rs. 20,000

• Time = 2 years

• Rate = 15 p.c.p.a

$\underline{\underline{\sf{\maltese\:To\:find\::-}}}$

• Compound interest

$\underline{\underline{\sf{\maltese\:Formula\:Used\::-}}}$

• Amount = P(1 + r/100)ⁿ

• Compound interest = Amount - Principal

$\underline{\underline{\sf{\maltese\:Concept\::-}}}$

$\odot$ Here we have given that the Principal is rs. 20000, Time is 2 years and rate is 15 p.c.p.a  . As we know that to find the compound interest we need Amount. So firstly we will find out the amount.

$\odot$ After finding the amount we will find out the Compound interest by substituting the values in the formula.

$\underline{\underline{\sf{\maltese\:Full\:Solution\::-}}}$

$\bigstar$ Let us find out the Amount by Substituting the values in the formula (Amount = P(1 + r/100)ⁿ.

$\qquad\sf{:\implies\:Amount\:=\:P\:\left(\:\dfrac{1\:+\:r}{100}\:\right)^n}$

$\qquad\sf{:\implies\:Amount\:=\:20000\:\left(\:\dfrac{1\:+\:15}{100}\:\right)^2}$

$\qquad\sf{:\implies\:Amount\:=\:20000\:\left(\:\dfrac{100\:+\:15}{100}\:\right)^2}$

$\qquad\sf{:\implies\:Amount\:=\:20000\:\left(\:\dfrac{115}{100}\:\right)^2}$

$\qquad\sf{:\implies\:Amount\:=\:20000\:\times\:\left(\:\dfrac{23}{20}\:\right)^2}$

$\qquad\sf{:\implies\:Amount\:=\:20000\:\times\:\left(\:\dfrac{23}{20}\:\right)\:\times\:\left(\:\dfrac{23}{20}\:\right)}$

$\qquad\sf{:\implies\:Amount\:=\:200\:\times\:\left(\:\dfrac{23}{2}\:\right)\:\times\:\left(\:\dfrac{23}{2}\:\right)}$

$\qquad\sf{:\implies\:Amount\:=\:26450}$

• Hence the amount is Rs. 26450 .

$\bigstar$  Let us find out the compound interest by substituting the values in the formula ( Compound interest = Amount - Principal )

$\qquad\sf{:\implies\:Compound\:interest\:=\:Amount\:-\:Principal}$

$\qquad\sf{:\implies\:Compound\:interest\:=\:26450\: -\: 20000}$

$\qquad\sf{:\implies\:Compound\:interest\:=\:6450}$

• Hence the compound interest is Rs. 6450

$\underline{\underline{\sf{\maltese\:Request\::-}}}$

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