Question

find the amount and the compound interest on rs 2000 at 10% p.a for 2½ year​

Answer 1

Answer:

Principal (P) = Rs.2000

Rate (R) = 10% p.a.

Time (T) = 2½ years = 5/2 years

Amount = P × (1 + R/100)^T

= 2000 × (1 + 10/100)^5/2

= 2000 × (11/10)^5/2

= Rs.2538.63

Hence, compound interest = Rs.(2538.63 - 2000) = Rs.538.63

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Answer 2

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

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• Principle = Rs. 2000
• Rate = 10%
• Time = 2½ years

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

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• Amount = ??

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

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• First we will findtge amount after 2 years

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

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$\sf : \implies\:{\bold{ Amount = 2000 \bigg( 1 + \dfrac{10}{100} \bigg) ^2 }}$

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$\sf : \implies\:{\bold{ Amount = 2000 \bigg( 1 + \dfrac{1}{10} \bigg) ^2 }}$

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$\sf : \implies\:{\bold{ Amount = 2000 \bigg( \dfrac{10 + 1 }{10} \bigg) ^2 }}$

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$\sf : \implies\:{\bold{ Amount = 2000 \bigg( \dfrac{11}{10} \bigg) ^2 }}$

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$\sf : \implies\:{\bold{ Amount = 2000 \times \dfrac{11\times 11}{10\times 10} }}$

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$\sf : \implies\:{\bold{ Amount = 200 \times \dfrac {11\times 11}{10} }}$

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$\sf : \implies\:{\bold{ Amount = 20 \times \dfrac {11\times 11}{1} }}$

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$\sf : \implies\:{\bold{ Amount = 20 \times{11\times 11} }}$

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$\sf : \implies\:{\bold{ Amount = 20 \times{121} }}$

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$\sf : \implies\:{\bold{ Amount = Rs. 2420}}$

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• Now we'll find the interest for the left half year

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$\sf{\red{\boxed{\bold{Amount = P + \dfrac{P\times R\times T}{100}}}}}$

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$\sf : \implies\:{\bold{ Amount = 2420 + \dfrac{2420\times 10 \times 1}{100\times 2} }}$

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$\sf : \implies\:{\bold{ Amount = 2420 + \dfrac{242\times 10 \times 1}{10\times 2} }}$

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$\sf : \implies\:{\bold{ Amount = 2420 + \dfrac{242\times 1}{ 2} }}$

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$\sf : \implies\:{\bold{ Amount = 2420 + 121 }}$

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$\sf : \implies\:{\bold{ Amount = Rs. 2541 }}$

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

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• Rs. 2000 after 2½ years at 10% per annum will amount to Rs. 2541