Question

Let us write the rate of compound interest per annum, so that the amount on 400 for 2 years becomes 441.

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Answer 1

||✪✪ QUESTION ✪✪||

Let us write the rate of compound interest per annum, so that the amount on 400 for 2 years becomes 441.

|| ✰✰ ANSWER ✰✰ ||

we know that, when Rate is compounded Annually ,

Amount = Principal * [ 1 + (R/100)]^T

Given That :-

→ Principal = Rs.400

→ Amount = Rs.441

→ Time = 2 years.

Putting all values in formula now, we get,

→ 441 = 400 [ 1 + (R/100) ]²

→ (441/400) = [ 1 + (R/100) ]²

→ (21/20)² = [ 1 + (R/100) ]²

Square - Root both sides ,

→ [ 1 + (R/100) ] = (21/20)

→ (R/100) = (21/20) - 1

→ (R/100) = 1/20

→ R = 5% .

Hence, Required Rate is 5% compounded Annually.

Answer 2

$\huge\frak{\underline{\underline{\pink{\:QUESTION}}}}$

Let us write the rate of compound interest per annum, so that the amount on 400 for 2 years becomes 441.

$\huge\frak{\underline{\underline{\pink{\:SOLUTION}}}}$

$\sf{\underline{\:GIVEN}}$

$\mapsto\sf{\pink{\:Principal\:=\:400\:rupees}}$

$\mapsto\sf{\pink{\:Amount\:=\:441\:rupees}}$

$\mapsto\sf{\pink{\:Time\:=\:2\:years}}$

$\sf{\underline{\:FIND}}$

$\mapsto\sf{\pink{\:Rate=\:?}}$

We Have,

FORMULA Of Amount ,when Rate in annual

$\boxed{\boxed{\orange{\sf{\:Amount\:=\:Principal\times\left[\:1+\dfrac{Rate}{100}\right]^{Time}}}}}$

$\:\:\:\:\:\:\small{\textsf{\green{\:( Keep above values )}}}$$\mapsto\sf{\:441\:=\:400\times\left[\:1+\dfrac{Rate}{100}\right]^{2}}$$\mapsto\sf{\sqrt{\dfrac{441}{400}}\:=\:\left[\:1+\dfrac{Rate}{100}\right]}$

$\mapsto\sf{\:\dfrac{21}{20}\:-\:1\:=\:\dfrac{Rate}{100}}$

$\mapsto\sf{\:\dfrac{21-20}{20}\:=\:\dfrac{Rate}{100}}$

$\mapsto\sf{\:\dfrac{1}{20}\:=\:\dfrac{Rate}{100}}$

$\mapsto\sf{\:\dfrac{1\times100}{20}\:=\:Rate}$

$\mapsto\sf{\:\dfrac{1\times\cancel{100}}{\cancel{20}}\:=\:Rate}$

$\mapsto\pink{\sf{\:Rate\:=\:5\:\%}}$

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Thus:-

★ Rate of compound interest per annum will be = 5%.

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