A sum of money lent at compound interest for 2 yr at 20 % pa would fetch ₹ 964 more, if the interest was payable half-yearly than if it was payable annually. What is the sum?

₹ 40000
₹ 60000
₹ 90000
₹ 500000

Correct Answer: ₹ 40000

Explanation:

Let the sum be ₹ P .
Then, CI when compounded half - yearly = [P x (1 + 10/100)⁴ - P] = 4641P/10000
CI when compounded annually = [ P x (1 + 20/100)² - P] = 11P/25
According to the question, 4641P/10000 - 11P/25 = 964
⇒ [(4641 - 4400)/10000] x P = 964
∴ P = (964 x 10000)/241
= ₹ 40000

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