Question

What will be the compound interest on ₹5000,if it is compounded half-yearly for 1 year 6 months at 8% per annum? ​

Answer 1

Compound interest would be Rs. 624.32.

Answer 2

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

• Principle = Rs. 5000
• Rate = 8%
• Time = 1year 6 months = 3half years

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

• Compound Interest = ?

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

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

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$\sf: \implies\: {\bold{ Amount = 5000\bigg( 1 +\dfrac{8}{100}\bigg)^3}}$

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$\sf: \implies\: {\bold{ Amount = 5000\bigg( \dfrac{100 + 8 }{100}\bigg)^3}}$

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$\sf: \implies\: {\bold{ Amount = 5000\bigg( \dfrac{108}{100}\bigg)^3}}$

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$\sf: \implies\: {\bold{ Amount = 5000\times\dfrac{108\times 108\times 108}{100\times 100 \times 100}}}$

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$\sf: \implies\: {\bold{ Amount = 50\times\dfrac{108\times 108\times 108}{100\times 100 }}}$

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$\sf: \implies\: {\bold{ Amount = 5\times\dfrac{108\times 108\times 108}{1000}}}$

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$\sf: \implies\: {\bold{ Amount = 5\times\dfrac{108\times 11664}{1000}}}$

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$\sf: \implies\: {\bold{ Amount = 5\times\dfrac{1259712}{1000}}}$

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$\sf: \implies\: {\bold{ Amount = \dfrac{ 6298560}{1000}}}$

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$\sf: \implies\: {\bold{ Amount = \dfrac{ 629856}{100}}}$

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$\sf: \implies\: {\bold{ Amount = Rs. 6298.56}}$

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

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$\sf: \implies\: {\bold{ CI = Rs. 6298.56 - Rs. 5000}}$

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$\sf: \implies\: {\bold{ CI = Rs. 1298.56}}$

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

• Rs. 5000 will earn Rs. 1298.56 as Compound Interest at 8% per annum in 1year 6 months when compounded half yearly