Question

Find the compound interest on Rs. 5000 for 3 years at 10% per annum. Also find the simple interest for Rs. 5000 for 3 years at 11%. Which is more and find the difference in the interests.​

Answer 1

$\sf{\bold{\huge{\underline{\blue{ Case\: 1 }}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Principle = Rs. 5000
• Time = 3 years
• Rate = 10%

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Compound Interest = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{Amount = p ( 1 + \dfrac{r}{100})^t}}}}$

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: $\sf\implies \: {\bold{ Amount = 5000 ( 1 + \dfrac{10}{100})^3}}$

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: $\sf\implies \: {\bold{ Amount = 5000 ( 1 + \dfrac{1}{10})^3}}$

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: $\sf\implies \: {\bold{ Amount = 5000 ( \dfrac{10 + 1 }{10})^3}}$

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: $\sf\implies \: {\bold{ Amount = 5000 ( \dfrac{11}{10})^3}}$

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: $\sf\implies \: {\bold{ Amount = 5000 ( \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10})}}$

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: $\sf\implies \: {\bold{ Amount = 500( \dfrac{11\times 11 \times 11}{10\times 10})}}$

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: $\sf\implies \: {\bold{ Amount = 50( \dfrac{11\times 11\times 11}{10})}}$

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: $\sf\implies \: {\bold{ Amount = 5 ( 11\times11 \times 11)}}$

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: $\sf\implies \: {\bold{ Amount = 5 \times 1331}}$

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: $\sf\implies \: {\bold{ Amount = Rs.6655}}$

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$\sf{\pink{\boxed{\bold{\dag Amount = Rs. 6655 }}}}$

$\sf{\red{\boxed{\bold{CI = Amount - Principle }}}}$

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:$\sf\implies\: {\bold{ CI = 6655 - 5000}}$

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:$\sf\implies\: {\bold{ CI = Rs. 1655}}$

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$\sf{\pink{\boxed{\bold{CI = Rs. 1655}}}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Rs. 5000 will have Rs .1655 as compound interest in 3 years at 10% per annum ⠀⠀

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$\sf{\bold{\huge{\underline{\blue{ Case\: 2 }}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Principle = Rs. 5000
• Rate = 11%
• Time = 3 years

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$\sf{\bold{\green{\underline{\underline{To\: find}}}}}$

• Simple interest = ???

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{SI = \dfrac{p\times r \times t }{100}}}}}$

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: $\sf\implies \: {\bold{ SI = \dfrac{5000\times 11\times 3}{100}}}$

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: $\sf\implies \: {\bold{ SI = 50\times 11\times 3}}$

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: $\sf\implies \: {\bold{ SI = 50\times 33}}$

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: $\sf\implies \: {\bold{ SI = Rs.1650}}$

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$\sf{\pink{\boxed{\bold{SI = Rs. 1650}}}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Rs. 5000 will have Rs.1650 as SI in 3 years at 11% per annum

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$\sf{\bold{\huge{\underline{\blue{ Compare }}}}}$

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CI = Rs. 1655

SI = Rs. 1650

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1655 > 1650

CI > SI

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Greater by = Rs. ( 1655 - 1650 )

Greater by = Rs. 5

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• CI is greater than SI by Rs. 5

Answer 2

Hope it's helpful dear