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

• A. Rs.10,000
• B. Rs.20,000
• C. Rs.40,000
• D. Rs.50,000

Answer 1

The Correct Option is B

Let the amount payable be P

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

⇒ $P(1+\frac{10}{100})^4-P$

⇒ $P[(\frac{11}{10})^4-1]$ ⇒ $P[\frac{14641-10000}{10000}]=\frac{4641}{10000}P$

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

⇒ $P(1+\frac{1}{5})^2-P$

⇒ $P(1+\frac{1}{5})^2-P$ ⇒ $P(\frac{6}{5})^2-P=P[(\frac{36}{5})-1]$

⇒ $P(\frac{11}{25})$

According to the given question,

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

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

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

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