Question

find the compound interest on Rupees 62500 at 8% per annum for 1 years , if the interest is compounded quarterly.​

Answer 1

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

• Principle = Rs. 62500
• Rate = 8%
• Time = 1 year = 4 quarterly

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

• Compound Interest = ??

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

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$\sf{\red{\boxed{\bold{Amount = P \bigg( 1 + \dfrac{r}{100}\bigg) ^2}}}}$

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$\sf : \implies\:{\bold{ Amount = 62500 \bigg( 1 + \dfrac{8}{100}\bigg)^4}}$

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$\sf : \implies\:{\bold{ Amount = 62500 \bigg( \dfrac{ 100 + 8}{100}\bigg)^4}}$

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$\sf : \implies\:{\bold{ Amount = 62500 \bigg( \dfrac{108}{100}\bigg)^4}}$

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$\sf : \implies\:{\bold{ Amount = 62500 \times \dfrac{108\times 108\times 108\times 108}{100\times 100 \times 100\times 100 }}}$

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$\sf : \implies\:{\bold{ Amount = 6250 \times \dfrac{108\times 108\times 108\times 108}{100\times 100 \times 100\times 10 }}}$

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$\sf : \implies\:{\bold{ Amount = 625\times \dfrac{108\times 108\times 108\times108}{100\times 100 \times 100 }}}$

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$\sf : \implies\:{\bold{ Amount = 625 \times \dfrac{11664\times 108\times108}{100\times 100 \times 100 }}}$

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$\sf : \implies\:{\bold{ Amount = 625 \times \dfrac{11664 \times 11664}{100\times 100 \times 100 }}}$

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$\sf : \implies\:{\bold{ Amount = 625 \times \dfrac{136048896}{100\times 100 \times 100 }}}$

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$\sf : \implies\:{\bold{ Amount = \dfrac{85030560000}{100\times 100 \times 100 }}}$

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ Amount = \dfrac{8503056000}{100\times 100 \times 10 }}}$

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$\sf : \implies\:{\bold{ Amount = \dfrac{850305600}{100\times 100 }}}$

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ Amount = \dfrac{85030560}{100\times 10 }}}$

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$\sf : \implies\:{\bold{ Amount = \dfrac{8503056}{100}}}$

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$\sf : \implies\:{\bold{ Amount = Rs. 85030.56}}$

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

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$\sf : \implies\:{\bold{ CI = Rs. 85030.56 - Rs. 62500 }}$

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$\sf : \implies\:{\bold{ CI = Rs. 22530. 56}}$

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

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• Rs. 62500 will earn Rs. 22530.56 as CI in 1 year at 8% compound interest compounded quarterly