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A sum of money is lent out at compound interest for two years at 20% per annum, compound interest being reckoned yearly. If the same sum of money was lent out at compound interest at the same rate per annum, compound interest being reckoned half-yearly, it would have fetched Rs. 482 more by way of interest in two years. Calculate the sum of money lent out.

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₹ 10000

₹ 14641

₹ 18732

₹ 20000

answer is D.

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Detailed Solution

compound interest being reckoned yearly

A = P {(1 + \frac{R}{100})}^{n} = P {(1 + \frac{20}{100})}^{2} = P (\frac{36}{25})

CI = A - P =

P (\frac{36}{25}) - P = P (\frac{11}{25})

compound interest being reckoned half-yearly

A = P {(1 + \frac{R}{200})}^{2 n} = P {(1 + \frac{20}{200})}^{2 \times 2} = P (\frac{14641}{10000})

CI = A - P =

P (\frac{14641}{10000}) - P = P (\frac{4641}{10000})

\Rightarrow P (\frac{4641}{10000}) - P (\frac{11}{25})

= 482

\Rightarrow P = \frac{482}{241} \times 10000 = 20000

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