Question

a sum of rupees 16000 is invested for three years at 10%p.a compounded annually. same amount invested for some period at simple interest.find the difference between the c.i and s.p​

Answer 1

AnswEr :

Rs.496.

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

A sum of Rs.16000 is invested for three years at 10% p.a. compounded annually, same amount invested for same period at simple Interest.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The difference between the C.I. and S.I.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

$\bf{We\:have}\begin{cases}\sf{Principal\:(P)=Rs.16000}\\ \sf{Rate\:(R)=10\%\:p.a.}\\ \sf{Time\:(T)=3\:years}\end{cases}}$

$\sf{\underline{\star\:{\large{\it{1st\:Case}}}}}$

Formula use : (For Compound Interest)

$\bf{\boxed{\bf{Compound\:Interest\:(C.I.)=A=P\bigg(1+\frac{R}{100} \bigg)^{n} }}}}$

$\mapsto\tt{A=16000\bigg(1+\dfrac{1\cancel{0}}{10\cancel{0}} \bigg)^{3} }\\\\\\\mapsto\tt{A=16000\bigg(\dfrac{10+1}{10} \bigg)^{3} }\\\\\\\mapsto\tt{A=16000\bigg(\dfrac{11}{10} \bigg)^{3} }\\\\\\\mapsto\tt{A=16\cancel{000}\times \dfrac{11}{1\cancel{0}} \times \dfrac{11}{1\cancel{0}} \times\dfrac{11}{1\cancel{0}}} \\\\\\\mapsto\tt{A=Rs.\big(16\times 11\times 11\times 11\big)}\\\\\\\mapsto\tt{\purple{A=Rs.21296}}$

We know that;

$\leadsto\sf{C.I.=A-P}\\\\\leadsto\sf{C.I.=Rs.21296-Rs.16000}\\\\\leadsto\sf{\purple{C.I.=Rs.5296}}$

______________________________________________

$\sf{\underline{\star\:{\large{\it{2nd\:Case}}}}}$

Formula use : (Simple Interest (S.I.)

$\bf{\boxed{\bf{Simple\:Interest\:(S.I.)=\frac{P\times R\times T}{100} }}}}$

$\mapsto\tt{S.I.=\dfrac{160\cancel{00}\times 10\times 3}{1\cancel{00}} }\\\\\\\mapsto\tt{S.I.=Rs.\big(160\times 10\times 3\big)}\\\\\\\mapsto\tt{\purple{S.I.=Rs.4800}}$

The difference between of the C.I. and S.I.

$\hookrightarrow\tt{Difference\:=\:C.I.-S.I.}\\\\\\\hookrightarrow\tt{Difference\:=\:Rs.5296-Rs.4800}\\\\\\\hookrightarrow\tt{\purple{Difference\:=\:Rs.496}}$

Answer 2

Answer:-

Given:

• Principle amount= Rs. 16000
• Time = 3years
• Interest rate = 10%

Need to find:

• Difference between compound and simple interest.

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$\huge{\bf{\underline{\red{SOLUTION}}}}$

The amount received after adding compound interest is :

$P \times {(1 + \frac{R}{100}) }^{n} \\ = 16000 \times {(1 + \frac{10}{100} )}^{3} \\ = 16000 \times ( \frac{110}{{100}})^{3} \\ = 16000 \times \frac{110}{100} \times \frac{110}{100} \times \frac{110}{100} \\ = 16 \times 11 \times 121 \\ = 176 \times 121$

=$\pink{\boxed{\boxed{=Rs.21296}}}$

Received Compound interest will be equal to:

=Amount received- Principle amount

=21296- 16000 Rs

=5296 rupees

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Simple interest is:

$\frac{PTR}{100} \\ = \frac{16000 \times 3 \times 10}{100}$

=$\pink{\boxed{\boxed{Rs.4800}}}$

━━━━━━━━━━━━

The difference is:

Compound interest- Simple Interest

=Rs.5296- 4800

=Rs.496

$\huge{\red{\boxed{\boxed{Answer=Rs.496}}}}$