Question:

A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs.482 more. If the interest was payable half yearly than if it was payable annually, the sum is

Updated On: Jan 30, 2025
  • Rs.10,000
  • Rs.20,000
  • Rs.40,000
  • Rs.50,000
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The Correct Option is B

Solution and Explanation

Let the amount payable be P

Compound interest when compounded half-yearly =P(1+R2×100)2tP=P(1+\frac{R}{2×100})^{2t}-P

⇒ P(1+10100)4PP(1+\frac{10}{100})^4-P

⇒ P[(1110)41]P[(\frac{11}{10})^4-1] ⇒ P[146411000010000]=464110000PP[\frac{14641-10000}{10000}]=\frac{4641}{10000}P

Compound interest when compounded annually =P(1+R100)tP=P(1+\frac{R}{100})^t-P

⇒ P(1+15)2PP(1+\frac{1}{5})^2-P

⇒ P(1+15)2PP(1+\frac{1}{5})^2-P ⇒ P(65)2P=P[(365)1]P(\frac{6}{5})^2-P=P[(\frac{36}{5})-1]

⇒ P(1125)P(\frac{11}{25})

According to the given question,

P(464110000)P(1125)=482P(\frac{4641}{10000})-P(\frac{11}{25})=482

P(4641440010000)=482P(\frac{4641-4400}{10000})=482

P=4820000241P=\frac{4820000}{241} (Or) P=20,000P=20,000

Hence, option B is the correct answer.The correct option is (B): Rs.20,000
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