Question: A sum of money lent at compound interest for 2 yr 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
Options:
A) Rs. 10000
B) Rs. 20000
C) Rs. 40000
D) Rs. 50000
Show Answer
Answer:
Correct Answer: B
Solution:
- Let the sum be Rs. x.
Then, CI when compounded half-yearly
$ =[ x\times {{( 1+\frac{10}{100} )}^{4}}-x ]=\frac{4641}{10000}x $
CI when compounded annually
$ =[ x\times {{( 1+\frac{20}{100} )}^{2}}-x ]=\frac{11}{25}x $
$ \therefore $ $ \frac{4641}{10000}x-\frac{11}{25}x=482 $
$ \Rightarrow $ $ x=\frac{482\times 10000}{241}=Rs.,20000 $